New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables
|
|
- Gwendolyn Arleen Cunningham
- 5 years ago
- Views:
Transcription
1 Journal of Mathematics and System Science 7 (017) doi: / / D DAVID PUBLISHING New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables Jambulingam Subramani and Master Ajith S Department of Statistics Ramanujan School of Mathematical sciences Pondicherry University Puducherry, , India id: drjsubramani@yahoo.co.in and ajith.master9@gmail.com Abstract This manuscript deals with new class of almost unbiased ratio cum product estimators for the estimation of population mean of the study variable by using the known values auxiliary variable. The bias and mean squared error of proposed estimators are obtained. An empirical study is carried out to assess the efficiency of proposed estimators over the existing estimators with the help of some known natural populations and it shows that the proposed estimators are almost unbiased and it perform better than the existing estimators. Keywords: Auxiliary variable, Bias, Mean squared error,natural populations, Ratio and Product estimators, Simple random sampling. 1. Introduction The efficiency of the estimators of the population parameters can be increased by using the prior information of the study characteristics. In literature several estimators exist with auxiliary variables involved. The commonly used thepopulation parameters of the auxiliary variables are mean, median, coefficient of variation, coefficient of skewness,coefficient of kurtosis etc. Ratio method of estimation is extensively used because of its computational simplicity and applicability.the correlation between study and auxiliary variables are negative the product method of estimation is used. Several researchers have directed their efforts towards to get efficient estimators of population mean. These estimators are biased but the percentage relative efficiency is better than that of simple random sampling, ratio and product estimators. For this reason, we consider the problem of estimation of population mean of study variable using known values of the auxiliary variable. So we have suggested new class modified ratio cum product estimators for estimating the population mean of the study variable. To know more abouthistorical developments of the estimation of population mean are referred to Cochran[1,], Subramani and Master Ajith [4,5], Murthy[7,8],Subramani[14], Subramani and kumarapandiyan[15,16,17], Upadhyaya and Singh[18], Yan and Tian[19] and the references cited there in. Consider a finite population U of size N consisting of UU 1, UU, UU 3. UU NN units. Each U i = (X i, Y i ),(i =1,,3...N) has a pair of values. Here Y be the study variable and X be the auxiliary variable which is correlated with Y. If yy = {yy 1, yy, yy yy nn }, and xx = {xx 1, xx, xx xx nn } be n sample values. Let yyand xx be the sample means of the study and auxiliary variables,ss yy = 1 NN (YY NN 1 ii=1 ii YY),SS xx = 1 NN (XX NN 1 ii=1 ii XX) and SS xxxx = 1 NN (YY NN 1 ii=1 ii YY)(XX ii XX) be the population variance and covariance of the study variable and auxiliary variable. Similarly the coefficient of variations and
2 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables coefficient of co-varianceof these variables are defined as CC yy = YY, CC xx = SS xx XX and CC xxxx = SS xxxx XXYY = ρρcc xx CC yy where is the correlation coefficient The simple random sample mean without replacement is used only when there is no additional information of the study variable is available,. In simple random sampling without replacement the estimator of population mean yy ssssss is an unbiased estimator for the population mean. The auxiliary variable and study variable are positively correlated,cochran [1]introduced ratio estimator for the estimation of population mean and it is given by YY RR = yy X = RRXX xx the bias and mean squared error of ratio estimator up to first order approximations are B(YY RR ) = δyy [CC xx ρρcc xx CC yy ] MSEYY RR = δyy CC yy + CC xx ρρccxx CC yy Where δ = 1 f n,ff = nn NN Some existing modified ratio estimators with their biases and mean squared errors are in table 1 Table 1: Bias and MSE of Existing modified ratio estimators Existing Estimators Constants Bias Variance/Mean squared Error YY MMMM1 = yy CC xxxx + ββ 1 CC xx xx + ββ 1 Yan and Tian [19] θθ 1 = CC xx XX CC xx XX + ββ 1 BYY MMMM1 = δyyθθ 1 CC xx θθ 1 ρc x C y MSEYY MMMM1 = δyy [CC yy + θθ 1 CCxx θθ 1 ρc x C y ] YY MMMM = yy ββ 1XX + CC xx ββ 1 xx + CC xx θθ = ββ 1 XX ββ 1 XX + CC xx BYY MMMM = δyyθθ CC xx θθ ρc x C y MSEYY MMMM = δyy [CC yy + θθ CCxx θθ ρc x C y ] YY MMMM3 = yy CC xxxx + ρρ CC xx xx + ρρ θθ 3 = CC xx XX CC xx XX + ρρ BYY MMMM3 = δyyθθ 3 CC xx θθ 3 ρc x C y MSEYY MMMM3 = δyy [CC yy + θθ 3 CCxx θθ 3 ρc x C y ] YY MMMM4 = yy ρρxx + CC xx ρρxx + CC xx θθ 4 = ρρxx ρρxx + CC xx BYY MMMM4 = δyyθθ 4 CC xx θθ 4 ρc x C y MSEYY MMMM4 = δyy [CC yy + θθ 4 CCxx θθ 4 ρc x C y ] YY MMMM5 = yy CC xxxx + ββ CC xx xx + ββ Upadhyaya and Singh [18] θθ 5 = CC xx XX CC xx XX + ββ BYY MMMM5 = δyyθθ 5 CC xx θθ 5 ρc x C y MSEYY MMMM5 = δyy [CC yy + θθ 5 CCxx θθ 5 ρc x C y ] YY MMMM6 = yy ββ XX + CC xx ββ xx + CC xx Upadhyaya and Singh [18] θθ 6 = ββ XX ββ XX + CC xx BYY MMMM6 = δyyθθ 6 CC xx θθ 6 ρc x C y MSEYY MMMM6 = δyy [CC yy + θθ 6 CCxx θθ 6 ρc x C y ] The auxiliary variable and study variable are negatively correlated, product estimator (Murthy[7]) is used,the bias and mean squared error of product estimator up to first order approximations are B(YY RR ) = δyy [ρρcc xx CC yy ] MSEYY RR = δyy CC yy + CC xx + ρρccxx CC yy
3 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables Existing Estimators YY MMMM1 = yy CC xxxx + ββ 1 CC xx XX + ββ 1 θθ 1 = YY MMMM = yy ββ 1xx + CC xx ββ 1 XX + CC xx θθ = Constants Bias Variance/Mean squared Error CC xx XX CC xx XX + ββ 1 BYY MMMM1 = δyyθθ 1 ρc x C y MSEYY MMMM1 = δyy [CC yy + θθ 1 CCxx + θθ 1 ρc x C y ] ββ 1 XX ββ 1 XX + CC xx BYY MMMM = δyyθθ ρc x C y MSEYY MMMM = δyy [CC yy + θθ CCxx + θθ ρc x C y ] YY MMMM3 = yy CC xxxx + ρρ CC xx XX + ρρ θθ 3 = CC xx XX CC xx XX + ρρ BYY MMMM3 = δyyθθ 3 ρc x C y MSEYY MMMM3 = δyy [CC yy + θθ 3 CCxx + θθ 3 ρc x C y ] YY MMMM4 = yy ρρxx + CC xx ρρxx + CC xx θθ 4 = YY MMMM5 = yy CC xxxx + ββ CC xx XX + ββ θθ 5 = YY MMMM6 = yy ββ xx + CC xx ββ XX + CC xx θθ 6 = ρρxx ρρxx + CC xx BYY MMMM4 = δyyθθ 4 ρc x C y MSEYY MMMM4 = δyy [CC yy + θθ 4 CCxx + θθ 4 ρc x C y ] CC xx XX CC xx XX + ββ BYY MMMM5 = δyyθθ 5 ρc x C y MSEYY MMMM3 = δyy [CC yy + θθ 5 CCxx + θθ 5 ρc x C y ] ββ XX ββ XX + CC xx BYY MMMM6 = δyyθθ 6 ρc x C y MSEYY MMMM = δyy [CC yy + θθ 6 CCxx + θθ 6 ρc x C y ] Some existing modified product estimators with their biases and mean squared errors are given in table Table : Bias and MSE of Existing modified product estimators. Suggested Class of Estimators In this section, new class of modified ratio cum product estimators for the population mean by using the known parameters of auxiliary variableis proposed and also derived the bias and the mean squared errors of the proposed estimators. The proposed estimators are given by YY PP1 = αα 1 λλ 1 yy CC xx XX+ββ 1 + (1 αα CC xx xx +ββ 1 )γγ 1 yy CC xx xx +ββ 1 1 CC xx XX+ββ 1 YY PP = αα λλ yy ββ 1XX+CC xx + (1 αα ββ 1 xx +CC )γγ yy ββ 1xx +CC xx xx ββ 1 XX+CC xx YY PP3 = αα 3 λλ 3 yy CC xx XX+ρρ + (1 αα CC xx xx +ρρ 3)γγ 3 yy CC xxxx +QQ rr CC xx XX+QQ rr YY PP4 = αα 4 λλ 4 yy ρρxx +CC xx + (1 αα ρρxx +CC 4 )γγ 4 yy ρρxx +CC xx xx ρρxx+cc xx YY PP5 = αα 5 λλ 5 yy CC xx XX+ββ + (1 αα CC xx xx +ββ 5 )γγ 5 yy CC xxxx +ββ CC xx XX+ββ YY PP6 = αα 6 λλ 6 yy ββ XX + CC xx ββ xx + CC xx + (1 αα 6 )γγ 6 yy ββ xx + CC xx ββ XX + CC xx Where λλ ii = γγ +aa ii CC ii =,i = 1,,3,4,5,6. Hereaa yy +bb ii CC ii sand bb ii s are constants. and CC yy are the yy population variance and coefficient of variation of study variable respectively. It is reasonable to assume that the values of and CC yy are known from the previous studies..1 The Bias and Mean Squared error of the Proposed Estimator
4 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables To obtain the bias and mean squared error of the proposed estimator, Consider ee 0 = yy YY, ee YY 1 = xx XX XX, θθ 1 = CC xx XX CC xx XX+ββ 1,θθ = ββ 1 XX ββ 1 XX+CC xx θθ 3 = CC xx XX CC xx XX+ρρ,θθ 4 = ρρxx ρρxx+cc xx,θθ 5 = CC xx XX CC xx XX+ββ,θθ 6 = ββ XX ββ XX+CC xx EE(ee 0 ) = EE(ee 1 ) = 0, EE(ee 0 ) = 1 ff YY CC nn yy, EE(ee 1 ) = 1 ff XX CC nn xx, EE(ee 0 ee 1 ) = 1 ff ρρcc nn xxcc yy Substitute the values of ee 0 and ee 1 in the proposed class of estimators and neglecting the higher order expressions, we get BBYY PPPP = EE(YY PPPP YY ) BBYY PPPP = 1 [YY (PP ii 1) + PP ii BBYY MMMMMM + BBYY MMMMMM + QQ ii BBYY MMMMMM BBYY MMMMMM ] WhereBYY MMMMMM = δyyθθ ii CC xx θθ ii ρc x C y, andbyy MMMMii = δyyθθ ii ρc x C y, i=1,,3,4, δ = 1 f n, θθ 1 = CC xx XX CC xx XX+ββ 1,θθ = ββ 1 XX ββ 1 XX+CC xx θθ 3 = CC xx XX CC xx XX+ρρ,θθ 4 = ρρxx ρρxx+cc xx,θθ 5 = Where PP ii = (αα ii λλ ii + (1 αα ii )γγ ii ) and QQ ii = (αα ii λλ ii (1 αα ii )γγ ii ) CC xx XX CC xx XX+ββ,θθ 6 = ββ XX ββ XX+CC xx Whereλλ ii and γγ ii are as defined above. If we assume that aa ii =0, bb ii = 0 and αα ii = 1 then the proposed estimators are exactly equal to the estimators given in Table 1.If aa ii =0, bb ii = 0 and αα ii = 0 then the proposed estimators are exactly equal to the estimators given in Table. If we assume that aa ii = BBYY MMMMMM, bb ii = BBYY MMMMMM, αα ii = 1 orαα ii = 0, then the proposed estimators are almost unbiased ratio estimators corresponding to the estimators given in Table 1 and. The detailed derivation of the mean squared errors are given in the appendix and the final expression is obtained with only first order approximation in the Taylor series expansion as, MMMMMMYY PPPP = EEYY PPPP YY MMMMMMYY PPPP = 1 4 [4YY (PP ii 1) + (PP ii + QQ ii ) MMMMMMYY MMMMMM + YYBBYY MMMMMM + (PP ii QQ ii ) MMMMMMYY MMMMMM + YYBBYY MMMMMM 4YY (PP ii + QQ ii )BBYY MMMMMM + (PP ii QQ ii )BBYY MMMMMM + PP ii QQ ii V(yy ssssss )] WhereBYY MMMMMM = δyyθθ ii CC xx θθ ii ρc x C y, BYY MMMMii = δyyθθ ii ρc x C y MSEYY MMMMii = δyy CC yy + θθ ii CCxx θθ ii ρc x C y MSEYY MMMMii = δyy CC yy + θθ ii CCxx + θθ ii ρc x C y andv(yy ssssss ) = δ = δδyy CC yy The optimal value of αα ii ss are determined by minimizing the MSE (YY pppp ) with respect to αα ii. For this differentiate MSE with respect to αα ii and equate to zero. = 0, and we get the value of αα ii, as αα ii
5 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables αα ii = Where λλ ii = YY (γγ ii 1)(γγ ii λλ ii ) + γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + YY λλ ii BBYY MMMMMM γγ ii BBYY MMMMMM λλ ii γγ ii V(yy ssssss ) YY (λλ ii γγ ii ) + λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM +aa ii CC yy, γγ ii = 3. Efficiency Comparison +bb ii CC yy,, i = 1,,3,4,5,6 If that aa ii = BBYY MMMMMM, bb ii = BBYY MMMMMM thenλλ ii = λλ ii γγ ii V(yy ssssss ) +BBYY MMMMMM CC yy, γγ ii = +BBYY MMMMMM CC yy,i = 1,,3,4,5,6. Substitute these values in the biased estimator and taking expectation we get the proposed estimators are almost unbiased.the efficiency comparison of the mean squared errorsof proposed estimatorsunder optimum conditions with that of the existing estimators are as follows 3.1 Comparison of Proposed estimators and Modified Ratio Estimator δyy CC yy + θθ ii CCxx θθ ii ρc x C y MMMMMMYY MMMMMM MMMMMMYY PPPP YY (αα ii λλ ii + (1 αα ii )γγ jj 1) + αα ii λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + (1 αα ii ) γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM YY αα ii λλ ii BBYY MMMMMM + (1 αα ii )γγ ii BBYY MMMMMM + (αα ii λλ ii (1 αα ii )γγ ii V(yy ssssss )) δyy CC yy + θθ ii CCxx θθ ii ρc x C y YY (αα ii λλ ii + (1 αα ii )γγ ii 1) + δyy CC yy (αα ii λλ ii + (1 αα ii )γγ ii ) + θθ CC xx 3αα ii λλ ii + (1 αα ii ) γγ ii αα ii λλ ii + θθθθcc xx CC yy (αα ii λλ ii (1 αα ii )γγ ii ) (αα ii λλ ii (1 αα ii ) γγ ii ) δδyy CC yy + θθ CC xx θθθθccxx CC yy YY (PP ii 1) + δδyy PP ii CC yy + θθ CC xx PP ii + (PP ii + QQ ii )(QQ ii 1) θθθθcc xx CC yy QQ ii (PP ii 1) δδδδδδcc xx CC yy (QQ ii (PP ii 1) 1) (PP ii 1) + δδ{cc yy PP ii 1 + θθ CC xx PP ii + (PP ii + QQ ii )(QQ ii 1) 1} ρρ (PP ii 1) + δδ[cc yy PP ii 1 + θθ CC xx PP ii + (PP ii + QQ ii )(PP ii 1) 1] δδδδcc xx CC yy (QQ ii (PP ii 1) 1) 3. Comparison of Proposed estimators and Modified Product Estimators MMMMMMYY MMMMMM MMMMMMYY PPPP
6 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables δyy CC yy + θθ ii CCxx + θθ ii ρc x C y YY (αα ii λλ ii + (1 αα ii )γγ jj 1) + αα ii λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + (1 αα ii ) γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM YY αα ii λλ ii BBYY MMMMMM + (1 αα ii )γγ ii BBYY MMMMMM + (αα ii λλ ii (1 αα ii )γγ ii V(yy ssssss )) δyy CC yy + θθ ii CCxx + θθ ii ρc x C y YY (αα ii λλ ii + (1 αα ii )γγ ii 1) + δyy CC yy (αα ii λλ ii + (1 αα ii )γγ ii ) + θθ CC xx 3αα ii λλ ii + (1 αα ii ) γγ ii αα ii λλ ii + θθθθcc xx CC yy (αα ii λλ ii (1 αα ii )γγ ii ) (αα ii λλ ii (1 αα ii ) γγ ii ) δδyy CC yy + θθ CC xx + θθθθccxx CC yy YY (PP ii 1) + δδyy PP ii CC yy + θθ CC xx PP ii + (PP ii + QQ ii )(PP ii 1) θθθθcc xx CC yy QQ ii (PP ii 1) δδδδδδcc xx CC yy (QQ ii (PP ii 1) + 1) (PP ii 1) + δδ{cc yy PP ii 1 + θθ CC xx PP ii + (PP ii + QQ ii )(QQ ii 1) 1} ρρ (PP ii 1) + δδ{cc yy PP ii 1 + θθ CC xx (PP ii (PP ii + QQ ii )(QQ ii 1) 1) δδδδcc xxxx (QQ ii (PP ii 1) + 1) 4. Numerical Study In this section we consider three natural populations,population 1 (Singh and Chaudhary [11] page 177),population (Khoshnevisan et.al.[6])and Population 3 (Cochran[] page 15) and are used to obtain the biases and mean squared errors and also used to compare the percentage relative efficiency of proposed estimator with that of the existing estimators.the computed values of constants and parameters of these populations are given below Table 3 : Parameters and Constants of Different Populations Constants Population 1 Population Population 3 N n YY XX SS xx CC xx CC yy ββ ββ ρρ θθ
7 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables θθ θθ θθ θθ θθ λλ λλ λλ λλ λλ λλ γγ γγ γγ γγ γγ γγ αα αα αα αα αα αα
8 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables Proposed Estimators Table 4:Bias and MSE of Proposed Estimators Population 1 Population Population 3 Bias MSE Bias MSE Bias MSE YY pp1 1.78E E E YY pp 7.11E E E YY pp3 4.6E E E YY pp4-1.60e E E YY pp5-1.07e E E YY pp6-1.78e E E Existing Estimators Table 5:Bias and MSE of Existing Estimators Population 1 Population Population 3 Bias MSE Bias MSE Bias MSE YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM YY MMMM Table 6: Percentage Relative Efficiency of Proposed Estimators Population 1 Population Population 3 Proposed Modified Modified Modified Modified Modified Modified Estimators Ratio Product Ratio Product Ratio Product YY pp YY pp YY pp YY pp YY pp YY pp
9 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables Conclusions In this paper we have suggested a new class of the modified ratio cum product estimators for finite population mean of the study variable Y with known parameters of the auxiliary variable. The biases and mean squared errors of the proposed estimators are obtained and compared with that of some existing modified ratio and modified product estimators.theoretically we have shown that the proposed estimator is always more efficient than other existing estimators under the optimum values of α i. and aa ii = BBYY MMMMMM, bb ii = BBYY MMMMMM. We have also studied the performance of the proposed estimators for certain known natural populations, it shows that the proposed estimator has less bias and mean squared error than all these existing estimators. That is the proposed estimator is more efficient than all these existing estimators. Hence we strongly recommended that the proposed estimator is more preferable than these existing estimators. References 1. Cochran W.G.(1940):The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce, The Journal of Agricultural Science, 30, Cochran, W. G. (1977):Sampling Techniques. Third Edition, Wiley Eastern Limited. 3. Jambulingam Subramani and Master Ajith (016):Improved Ratio cum Product Estimator with Known Coefficient of Variation insimple Random SamplingJ. Adv. Res. Appl. Math. Stat.; 1(), Jambulingam Subramani and Master Ajith (016):Modified Ratio cum Product Estimators for Estimation of Finite Population Mean with Known Correlation Coefficient Biom. Biostat. Int J, 4(6): Khoshnevisan M., Singh R., Chauhan P., Sawan N. and Smarandache F. (007): A general family of estimators for estimating population mean using known value of some population parameter(s), Far East Journal of Theoretical Statistics, Murthy, M.N. (1964): Product method of estimation. Sankhya A, 6, Murthy, M.N. (1967): Sampling theory and methods. Statistical Publishing Society, Calcutta, India 8. Rajesh Tailor and Balkishan Sharma (009): A Modified Ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis statistics in transition, July Vol. 10, No. 1, pp Ramkrishna S. Solanki, Housila P. Singh and Surya K. Pal (015): Improved ratio-type estimators of finite population variance using quartiles, Hacettepe Journal of Mathematics and Statistics Volume 44 (3) Singh, D. and Chaudhary, F.S. (1986):Theory and analysis of sample survey designs. New Age International Publisher 11. Singh, H. P. and Agnihotri, N.(008): A general procedure of estimating population mean using auxiliary information in sample surveys. Statistics in Transition- new series, 9, Singh, H.P., Tailor, R., Tailor, R. and Kakran, M.S.(004):Animproved estimator of population mean using power transformation. Journal of the Indian Society of Agricultural Statistics, 58(), 3-30,
10 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables 13. Sisodia B.V.S. and V.K. Dwivedi (1981): A modified ratio estimator using coefficient of variation of auxiliary variable, Jour. Ind. Soc. Agri. Stat., Vol. 33(1), Pp , 14. Subramani, J (013): "Generalized modified ratio estimator for estimation of finite population mean," Journal of Modern Applied Statistical Methods, vol.1, pp Subramani J.and G. Kumarapandiyan (01): Modified Ratio Estimators for Population Mean Using Function of Quartiles of Auxiliary Variable, Bonfring International Journal of Industrial Engineering and Management Science, Vol., No., 16. Subramani, J.,and Kumarapandiyan, (01) G. Variance estimation using quartiles and their functionsof an auxiliary variable, International Journal of Statistics and Applications (5), Subramani and G.Kumarapandiyan (01): A class of almost unbiased modified ratio estimators for population mean withknown population parameters;elixir Statistics Upadhyaya, L.N. and Singh, H.P(1999): Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal 41 (5), , 19. Yan, Z. and Tian, B. (010): Ratio Method to the Mean Estimation Using Co-efficient of Skewness of Auxiliary Variable, ICICA 010, Part II, CCIS 106, pp
11 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables Bias and MSE of Proposed Estimators APPENDIX The proposed class of ratio cum product estimators with known parameters of auxiliary variables are YY PP1 = αα 1 λλ 1 yy CC xx XX+ββ 1 + (1 αα CC xx xx +ββ 1 )γγ 1 yy CC xx xx +ββ 1 1 CC xx XX+ββ 1 YY PP = αα λλ yy ββ 1XX+CC xx + (1 αα ββ 1 xx +CC )γγ yy ββ 1xx +CC xx xx ββ 1 XX+CC xx YY PP3 = αα 3 λλ 3 yy CC xx XX+ρρ + (1 αα CC xx xx +ρρ 3)γγ 3 yy CC xxxx +QQ rr CC xx XX+QQ rr YY PP4 = αα 4 λλ 4 yy ρρxx +CC xx + (1 αα ρρxx +CC 4 )γγ 4 yy ρρxx +CC xx xx ρρxx+cc xx YY PP5 = αα 5 λλ 5 yy CC xx XX+ββ + (1 αα CC xx xx +ββ 5 )γγ 5 yy CC xxxx +ββ CC xx XX+ββ YY PP6 = αα 6 λλ 6 yy ββ XX + CC xx ββ xx + CC xx + (1 αα 6 )γγ 6 yy ββ xx + CC xx ββ XX + CC xx Where λλ ii = γγ +aa ii CC ii =, i = 1,,3,4,5,6 yy +bb ii CC yy To obtain the bias and mean squared error of the proposed estimators, Consider,ee 0 = yy YY, ee YY 1 = xx XX, δ = 1 ff XX,ff = nn nn NN CC θθ 1 = xx XX ββ,θθ CC xx XX+ββ = 1 XX CC θθ 1 ββ 1 XX+CC 3 = xx XX,θθ ρρxx CC xx CC xx XX+ρρ 4 =,θθ ρρxx+cc 5 = xx XX ββ,θθ xx CC xx XX+ββ 6 = XX Where i = 1,,3,4,5,6 ββ XX+CC xx EE(ee 0 ) = EE(ee 1 ) = 0, EE(ee 0 ) = δyy CC yy, EE(ee 1 ) = δxx CC xx, EE(ee 0 ee 1 ) = δρρcc xx CC yy Substitute these values in YY pppp and neglecting the higher order expressions, we get YY pppp = αα ii λλ ii YY(1 + ee 0 )(1 + θθ ii ee 1 ) 1 + (1 αα ii )γγ ii YY(1 + ee 0 )(1 + θθ ii ee 1 ) = YYαα ii λλ ii (1 + ee 0 )(1 θθ ii ee 1 + θθ ii ee 1 ) + (1 αα ii )γγ ii (1 + ee 0 )(1 + θθ ii ee 1 ) = YYαα ii λλ ii (1 θθ ii ee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 ) + (1 αα ii )γγ ii (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) YY pppp YY = YYαα ii λλ ii 1 θθ ii ee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 + (1 αα ii )γγ ii (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) BBYY PPPP = EE(YY PPPP YY ) = EEYY(αα ii λλ ii (1 θθ ii ee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 ) + (1 αα ii )γγ ii (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) 1)} = δyyαα ii λλ ii (1 + θθ ii CC xx θθ ii ρρcc xx CC yy ) + (1 αα ii )γγ ii 1 + θθ ii ρρcc xx CC yy 1
12 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables BBYY PPPP = YY(αα ii λλ ii + (1 αα ii )γγ ii 1} + αα ii λλ ii BBYY MMMMMM + (1 αα ii )γγ ii BBYY MMMMMM Take a substitution PP ii = (αα ii λλ ii + (1 αα ii )γγ ii ) and QQ ii = (αα ii λλ ii (1 αα ii )γγ ii ) then BBYY PPPP = YY(PP ii 1} + (PP ii + QQ ii ) BBYY MMMMMM + (PP ii QQ ii ) BBYY MMMMMM BBYY PPPP = 1 [YY (PP ii 1) + PP ii BBYY MMMMMM + BBYY MMMMMM + QQ ii BBYY MMMMMM BBYY MMMMMM ] The mean squared errors of the proposed estimatorsare MMMMMMYY PPPP = EEYY PPPP YY = EE{YY(αα ii λλ ii (1 θθ ii ee 1 + θθ ee 1 + ee 0 θθ ii ee 1 ee 0 ) + (1 αα ii )γγ ii (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) 1) } = EE YY (αα ii λλ ii 1 θθ ii ee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 + (1 αα ii ) γγ ii (1 + θθ ii ee 1 + θθ ii ee 0 ee 1 ) αα ii λλ ii (1 αα ii )γγ ii 1 θθ ii ee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) αα ii λλ ii 1 θθee 1 + θθ ii ee 1 + ee 0 θθ ii ee 1 ee 0 (1 αα ii )γγ ii (1 + θθ ii ee 1 + ee 0 + θθ ii ee 0 ee 1 ) = δyy αα ii λλ ii 1 + 3θθ ii CC xx + CC yy 4θθ ii ρρcc xx CC yy + (1 αα ii ) γγ ii 1 + θθ ii θθ CC xx + CC yy + 4θθ ii ρρcc xx CC yy + αα ii λλ ii (1 αα ii )γγ ii 1 + CC yy αα ii λλ ii 1 + θθ ii CC xx θθ ii ρρcc xx CC yy (1 αα ii )γγ ii 1 + θθ ii ρρcc xx CC yy MMMMMMYY PPPP = YY (αα ii λλ ii + (1 αα ii )γγ ii 1) + αα ii λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + (1 αα ii ) γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM YY αα ii λλ ii BBYY MMMMMM + (1 αα ii )γγ ii BBYY MMMMMM + (αα ii λλ ii (1 αα ii )γγ ii V(yy ssssss ) MMMMMMYY PPPP = YY (PP ii 1) + αα ii λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + (1 αα ii ) γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM YY αα ii λλ ii BBYY MMMMMM + (1 αα ii )γγ ii BBYY MMMMMM + (αα ii λλ ii (1 αα ii )γγ ii V(yy ssssss ) We take a substitution PP ii = (αα ii λλ ii + (1 αα ii )γγ ii ) and QQ ii = (αα ii λλ ii (1 αα ii )γγ ii ) then the MSE is MMMMMMYY PPPP = YY (PP ii 1) + (PP ii + QQ ii ) MMMMMMYY 4 MMMMMM + YYBBYY MMMMMM + (PP ii QQ ii ) MMMMMMYY 4 MMMMMM + YYBBYY MMMMMM YY (PP ii + QQ ii ) BBYY MMMMMM + (PP ii QQ ii ) BBYY MMMMMM + PP ii QQ ii V(yy 4 ssssss )] MMMMMMYY PPPP = 1 4 [4YY (PP ii 1) + (PP ii + QQ ii ) MMMMMMYY MMMMMM + YYBBYY MMMMMM + (PP ii QQ ii ) MMMMMMYY MMMMMM + YYBBYY MMMMMM 4YY (PP ii + QQ ii )BBYY MMMMMM + (PP ii QQ ii )BBYY MMMMMM + PP ii QQ ii V(yy ssssss )]
13 New Class of Almost Unbiased Modified Ratio Cum Product Estimators with Knownparameters of Auxiliary Variables WhereBYY MMMMMM = δyyθθ ii CC xx θθ ii ρc x C y,byy MMMMii = δyyθθ ii ρc x C y MSEYY MMMMii = δyy CC yy + θθ ii CCxx θθ ii ρc x C y MSEYY MMMMii = δyy CC yy + θθ ii CCxx + θθ ii ρc x C y andv(yy ssssss ) = δ = δδyy CC yy CC xx XX δ = 1 f, θθ n 1 =,θθ CC xx XX+ββ = 1 where, i = 1,,3,4,5,6 ββ 1 XX ββ 1 XX+CC xx θθ 3 = CC xx XX CC xx XX+ρρ,θθ 4 = ρρxx ρρxx+cc xx,θθ 5 = CC xx XX CC xx XX+ββ,θθ 6 = ββ XX ββ XX+CC xx The optimal value of αα ii is determined by minimize the MSE (YY pppp ) with respect to αα ii. For this differentiate MSE with respect to αα ii and equate to zero. ie, = 0, and we get the value of αα αα ii, as ii YY (αα ii λ i + (1 αα ii )γγ ii 1)(λ i γγ ii ) + αα ii λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM ) (1 αα ii )γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM ) YY λλ ii BBYY MMMMMM + γγ ii BBYY MMMMMM + (λλ ii (1 αα ii )γγ ii V(yy ssssss ) = 0 αα ii = (YY (γγ ii 1)(γγ ii λλ ii ) + γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + YY λλ ii BBYY MMMMMM γγ ii BBYY MMMMMM λλ ii γγ ii V(yy ssssss )) (YY (λλ ii γγ ii ) + λλ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM + γγ ii MMMMMMYY MMMMMM + YYBBYY MMMMMM Where δ = 1 f, i = 1,,3,4,5,6 n λλ ii γγ ii V(yy ssssss ))
A Class of Regression Estimator with Cum-Dual Ratio Estimator as Intercept
International Journal of Probability and Statistics 015, 4(): 4-50 DOI: 10.593/j.ijps.015040.0 A Class of Regression Estimator with Cum-Dual Ratio Estimator as Intercept F. B. Adebola 1, N. A. Adegoke
More informationUse of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling
International Journal of Statistics and Probability; Vol. 5, No. 3; May 2016 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education Use of Auxiliary Variables and Asymptotically
More informationThe Simple Linear Regression Model ECONOMETRICS (ECON 360) BEN VAN KAMMEN, PHD
The Simple Linear Regression Model ECONOMETRICS (ECON 360) BEN VAN KAMMEN, PHD Outline Definition. Deriving the Estimates. Properties of the Estimates. Units of Measurement and Functional Form. Expected
More informationECO 745: Theory of International Economics. Jack Rossbach Fall Lecture 6
ECO 745: Theory of International Economics Jack Rossbach Fall 2015 - Lecture 6 Review We ve covered several models of trade, but the empirics have been mixed Difficulties identifying goods with a technological
More informationMidterm Exam 1, section 2. Thursday, September hour, 15 minutes
San Francisco State University Michael Bar ECON 312 Fall 2018 Midterm Exam 1, section 2 Thursday, September 27 1 hour, 15 minutes Name: Instructions 1. This is closed book, closed notes exam. 2. You can
More informationOperational Risk Management: Preventive vs. Corrective Control
Operational Risk Management: Preventive vs. Corrective Control Yuqian Xu (UIUC) July 2018 Joint Work with Lingjiong Zhu and Michael Pinedo 1 Research Questions How to manage operational risk? How does
More informationSpecial Topics: Data Science
Special Topics: Data Science L Linear Methods for Prediction Dr. Vidhyasaharan Sethu School of Electrical Engineering & Telecommunications University of New South Wales Sydney, Australia V. Sethu 1 Topics
More informationMixture Models & EM. Nicholas Ruozzi University of Texas at Dallas. based on the slides of Vibhav Gogate
Mixture Models & EM Nicholas Ruozzi University of Texas at Dallas based on the slides of Vibhav Gogate Previously We looked at -means and hierarchical clustering as mechanisms for unsupervised learning
More informationISyE 6414 Regression Analysis
ISyE 6414 Regression Analysis Lecture 2: More Simple linear Regression: R-squared (coefficient of variation/determination) Correlation analysis: Pearson s correlation Spearman s rank correlation Variable
More informationNew Numerical Schemes for the Solution of Slightly Stiff Second Order Ordinary Differential Equations
American Journal of Computational and Applied Mathematics 24, 4(6): 239-246 DOI:.5923/j.ajcam.2446.7 New Numerical Schemes for the Solution of Slightly Stiff Second Order Ordinary Differential Equations
More informationLecture 5. Optimisation. Regularisation
Lecture 5. Optimisation. Regularisation COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne Iterative optimisation Loss functions Coordinate
More informationAnalysis of Gini s Mean Difference for Randomized Block Design
American Journal of Mathematics and Statistics 2015, 5(3): 111-122 DOI: 10.5923/j.ajms.20150503.02 Analysis of Gini s Mean Difference for Randomized Block Design Elsayed A. H. Elamir Department of Statistics
More informationBayesian Methods: Naïve Bayes
Bayesian Methods: Naïve Bayes Nicholas Ruozzi University of Texas at Dallas based on the slides of Vibhav Gogate Last Time Parameter learning Learning the parameter of a simple coin flipping model Prior
More informationJasmin Smajic 1, Christian Hafner 2, Jürg Leuthold 2, March 16, 2015 Introduction to Finite Element Method (FEM) Part 1 (2-D FEM)
Jasmin Smajic 1, Christian Hafner 2, Jürg Leuthold 2, March 16, 2015 Introduction to Finite Element Method (FEM) Part 1 (2-D FEM) 1 HSR - University of Applied Sciences of Eastern Switzerland Institute
More informationCombining Experimental and Non-Experimental Design in Causal Inference
Combining Experimental and Non-Experimental Design in Causal Inference Kari Lock Morgan Department of Statistics Penn State University Rao Prize Conference May 12 th, 2017 A Tribute to Don Design trumps
More informationLogistic Regression. Hongning Wang
Logistic Regression Hongning Wang CS@UVa Today s lecture Logistic regression model A discriminative classification model Two different perspectives to derive the model Parameter estimation CS@UVa CS 6501:
More informationImperfectly Shared Randomness in Communication
Imperfectly Shared Randomness in Communication Madhu Sudan Harvard Joint work with Clément Canonne (Columbia), Venkatesan Guruswami (CMU) and Raghu Meka (UCLA). 11/16/2016 UofT: ISR in Communication 1
More informationOperations on Radical Expressions; Rationalization of Denominators
0 RD. 1 2 2 2 2 2 2 2 Operations on Radical Expressions; Rationalization of Denominators Unlike operations on fractions or decimals, sums and differences of many radicals cannot be simplified. For instance,
More informationProduct Decomposition in Supply Chain Planning
Mario R. Eden, Marianthi Ierapetritou and Gavin P. Towler (Editors) Proceedings of the 13 th International Symposium on Process Systems Engineering PSE 2018 July 1-5, 2018, San Diego, California, USA 2018
More informationknn & Naïve Bayes Hongning Wang
knn & Naïve Bayes Hongning Wang CS@UVa Today s lecture Instance-based classifiers k nearest neighbors Non-parametric learning algorithm Model-based classifiers Naïve Bayes classifier A generative model
More informationCourse 495: Advanced Statistical Machine Learning/Pattern Recognition
Course 495: Advanced Statistical Machine Learning/Pattern Recognition Lectures: Stefanos Zafeiriou Goal (Lectures): To present modern statistical machine learning/pattern recognition algorithms. The course
More informationJamming phenomena of self-driven particles
Jamming phenomena of self-driven particles Pedestrian Outflow and Obstacle Walking with Slow Rhythm Daichi Yanagisawa, RCAST, UTokyo Pedestrian Outflow and Obstacle Phys. Rev. E, 76(6), 061117, 2007 Phys.
More informationSNARKs with Preprocessing. Eran Tromer
SNARKs with Preprocessing Eran Tromer BIU Winter School on Verifiable Computation and Special Encryption 4-7 Jan 206 G: Someone generates and publishes a common reference string P: Prover picks NP statement
More informationTie Breaking Procedure
Ohio Youth Basketball Tie Breaking Procedure The higher seeded team when two teams have the same record after completion of pool play will be determined by the winner of their head to head competition.
More informationLecture 10. Support Vector Machines (cont.)
Lecture 10. Support Vector Machines (cont.) COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Soft margin SVM Intuition and problem
More informationSupport Vector Machines: Optimization of Decision Making. Christopher Katinas March 10, 2016
Support Vector Machines: Optimization of Decision Making Christopher Katinas March 10, 2016 Overview Background of Support Vector Machines Segregation Functions/Problem Statement Methodology Training/Testing
More informationFailure Data Analysis for Aircraft Maintenance Planning
Failure Data Analysis for Aircraft Maintenance Planning M. Tozan, A. Z. Al-Garni, A. M. Al-Garni, and A. Jamal Aerospace Engineering Department King Fahd University of Petroleum and Minerals Abstract This
More informationISyE 6414: Regression Analysis
ISyE 6414: Regression Analysis Lectures: MWF 8:00-10:30, MRDC #2404 Early five-week session; May 14- June 15 (8:00-9:10; 10-min break; 9:20-10:30) Instructor: Dr. Yajun Mei ( YA_JUNE MAY ) Email: ymei@isye.gatech.edu;
More informationPre-Kindergarten 2017 Summer Packet. Robert F Woodall Elementary
Pre-Kindergarten 2017 Summer Packet Robert F Woodall Elementary In the fall, on your child s testing day, please bring this packet back for a special reward that will be awarded to your child for completion
More informationTSP at isolated intersections: Some advances under simulation environment
TSP at isolated intersections: Some advances under simulation environment Zhengyao Yu Vikash V. Gayah Eleni Christofa TESC 2018 December 5, 2018 Overview Motivation Problem introduction Assumptions Formation
More informationAnalysis of Shear Lag in Steel Angle Connectors
University of New Hampshire University of New Hampshire Scholars' Repository Honors Theses and Capstones Student Scholarship Spring 2013 Analysis of Shear Lag in Steel Angle Connectors Benjamin Sawyer
More informationCalibration and Validation of the Shell Fatigue Model Using AC10 and AC14 Dense Graded Hot Mix Asphalt Fatigue Laboratory Data
Article Calibration and Validation of the Shell Fatigue Model Using AC10 and AC14 Dense Graded Hot Mix Asphalt Fatigue Laboratory Data Mofreh Saleh University of Canterbury, Private Bag 4800, Christchurch,
More informationMinimum Mean-Square Error (MMSE) and Linear MMSE (LMMSE) Estimation
Minimum Mean-Square Error (MMSE) and Linear MMSE (LMMSE) Estimation Outline: MMSE estimation, Linear MMSE (LMMSE) estimation, Geometric formulation of LMMSE estimation and orthogonality principle. Reading:
More informationWhat is Restrained and Unrestrained Pipes and what is the Strength Criteria
What is Restrained and Unrestrained Pipes and what is the Strength Criteria Alex Matveev, September 11, 2018 About author: Alex Matveev is one of the authors of pipe stress analysis codes GOST 32388-2013
More informationRunning head: DATA ANALYSIS AND INTERPRETATION 1
Running head: DATA ANALYSIS AND INTERPRETATION 1 Data Analysis and Interpretation Final Project Vernon Tilly Jr. University of Central Oklahoma DATA ANALYSIS AND INTERPRETATION 2 Owners of the various
More informationSan Francisco State University ECON 560 Summer Midterm Exam 2. Monday, July hour 15 minutes
San Francisco State University Michael Bar ECON 560 Summer 2018 Midterm Exam 2 Monday, July 30 1 hour 15 minutes Name: Instructions 1. This is closed book, closed notes exam. 2. No calculators or electronic
More informationLegendre et al Appendices and Supplements, p. 1
Legendre et al. 2010 Appendices and Supplements, p. 1 Appendices and Supplement to: Legendre, P., M. De Cáceres, and D. Borcard. 2010. Community surveys through space and time: testing the space-time interaction
More informationNovel empirical correlations for estimation of bubble point pressure, saturated viscosity and gas solubility of crude oils
86 Pet.Sci.(29)6:86-9 DOI 1.17/s12182-9-16-x Novel empirical correlations for estimation of bubble point pressure, saturated viscosity and gas solubility of crude oils Ehsan Khamehchi 1, Fariborz Rashidi
More informationNCSS Statistical Software
Chapter 256 Introduction This procedure computes summary statistics and common non-parametric, single-sample runs tests for a series of n numeric, binary, or categorical data values. For numeric data,
More informationInfluence of Forecasting Factors and Methods or Bullwhip Effect and Order Rate Variance Ratio in the Two Stage Supply Chain-A Case Study
International Journal of Engineering and Technical Research (IJETR) ISSN: 31-0869 (O) 454-4698 (P), Volume-4, Issue-1, January 016 Influence of Forecasting Factors and Methods or Bullwhip Effect and Order
More informationFunctions of Random Variables & Expectation, Mean and Variance
Functions of Random Variables & Expectation, Mean and Variance Kuan-Yu Chen ( 陳冠宇 ) @ TR-409, NTUST Functions of Random Variables 1 Given a random variables XX, one may generate other random variables
More informationCS249: ADVANCED DATA MINING
CS249: ADVANCED DATA MINING Linear Regression, Logistic Regression, and GLMs Instructor: Yizhou Sun yzsun@cs.ucla.edu April 24, 2017 About WWW2017 Conference 2 Turing Award Winner Sir Tim Berners-Lee 3
More informationANALYSIS OF ACCIDENT SURVEY ON PEDESTRIANS ON NATIONAL HIGHWAY 16 USING STATISTICAL METHODS
ANALYSIS OF ACCIDENT SURVEY ON PEDESTRIANS ON NATIONAL HIGHWAY 16 USING STATISTICAL METHODS K.SWETHA Assistant Professor Civil Department, Sai Ganapati Engineering College, JNTUK, Visakhapatnam, India,
More informationValidatingWindProfileEquationsduringTropicalStormDebbyin2012
Global Journal of Researches in Engineering: e Civil And Structural Engineering Volume 4 Issue Version. Year 24 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationChapter 10 Aggregate Demand I: Building the IS LM Model
Chapter 10 Aggregate Demand I: Building the IS LM Model Zhengyu Cai Ph.D. Institute of Development Southwestern University of Finance and Economics All rights reserved http://www.escience.cn/people/zhengyucai/index.html
More informationCAPACITY ESTIMATION OF URBAN ROAD IN BAGHDAD CITY: A CASE STUDY OF PALESTINE ARTERIAL ROAD
VOL. 13, NO. 21, NOVEMBER 218 ISSN 1819-668 26-218 Asian Research Publishing Network (ARPN). All rights reserved. CAPACITY ESTIMATION OF URBAN ROAD IN BAGHDAD CITY: A CASE STUDY OF PALESTINE ARTERIAL ROAD
More informationINTRODUCTION Microfilm copy of the Draper Collection of manuscripts. Originals located at the State Historical Society of Wisconsin.
C Draper, Lyman Copeland, Collection, 1735-1815 2964 136 rolls of microfilm RESTRICTED MICROFILM This collection is available at The State Historical Society of Missouri. If you would like more information,
More informationNorthwest Fishery Resource Bulletin
Northwest Fishery Resource Bulletin Estimating the Harvest of Salmon by the Marine Sport Fishery in Puget Sound: Evaluation and Recommendations by Robert H. Conrad Northwest Indian Fisheries Commission
More informationThe Effect of Public Sporting Expenditures on Medal Share at the Summer Olympic Games: A Study of the Differential Impact by Sport and Gender
Dickinson College Dickinson Scholar Student Honors Theses By Year Student Honors Theses 5-21-2017 The Effect of Public Sporting Expenditures on Medal Share at the Summer Olympic Games: A Study of the Differential
More informationThe Estimation of Winners Number of the Olympiads Final Stage
Olympiads in Informatics, 15, Vol. 9, 139 145 DOI: http://dx.doi.org/1.15388/ioi.15.11 139 The Estimation of Winners Number of the Olympiads Final Stage Aleksandr MAIATIN, Pavel MAVRIN, Vladimir PARFENOV,
More informationGamblers Favor Skewness, Not Risk: Further Evidence from United States Lottery Games
Gamblers Favor Skewness, Not Risk: Further Evidence from United States Lottery Games Thomas A. Garrett Russell S. Sobel Department of Economics West Virginia University Morgantown, West Virginia 26506
More informationFull Name: Period: Heredity EOC Review
Full Name: Period: 1 4 5 6 7 Heredity EOC Review Directions: For each genotype below, indicate whether it is a heterozygous (write: He) OR homozygous (write: Ho). 1. Tt BB DD ff tt dd dd Ff TT Bb bb FF
More informationName May 3, 2007 Math Probability and Statistics
Name May 3, 2007 Math 341 - Probability and Statistics Long Exam IV Instructions: Please include all relevant work to get full credit. Encircle your final answers. 1. An article in Professional Geographer
More informationAquaculture Technology - PBBT301 UNIT I - MARINE ANIMALS IN AQUACULTURE
Aquaculture Technology - PBBT301 UNIT I - MARINE ANIMALS IN AQUACULTURE PART A 1. Define aquaculture. 2. Write two objectives of aquaculture? 3. List the types of aquaculture. 4. What is monoculture? 5.
More informationCritical Gust Pressures on Tall Building Frames-Review of Codal Provisions
Dr. B.Dean Kumar Dept. of Civil Engineering JNTUH College of Engineering Hyderabad, INDIA bdeankumar@gmail.com Dr. B.L.P Swami Dept. of Civil Engineering Vasavi College of Engineering Hyderabad, INDIA
More informationTeam formation and selection of strategies for computer simulations of baseball gaming
Team formation and selection of strategies for computer simulations of baseball gaming ARTURO YEE 1, MATÍAS ALVARADO 2 AND GERMINAL COCHO 3 1 Faculty of Informatics, Universidad Autónoma de Sinaloa. Calle
More informationIDENTIFYING SUBJECTIVE VALUE IN WOMEN S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIO-ECONOMIC CLASS. Victoria Allred
IDENTIFYING SUBJECTIVE VALUE IN WOMEN S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIO-ECONOMIC CLASS by Victoria Allred A Senior Honors Project Presented to the Honors College East Carolina University In
More informationThree New Methods to Find Initial Basic Feasible. Solution of Transportation Problems
Applied Mathematical Sciences, Vol. 11, 2017, no. 37, 1803-1814 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.75178 Three New Methods to Find Initial Basic Feasible Solution of Transportation
More informationAddition and Subtraction of Rational Expressions
RT.3 Addition and Subtraction of Rational Expressions Many real-world applications involve adding or subtracting algebraic fractions. Similarly as in the case of common fractions, to add or subtract algebraic
More informationy ) s x x )(y i (x i r = 1 n 1 s y Statistics Lecture 7 Exploring Data , y 2 ,y n (x 1 ),,(x n ),(x 2 ,y 1 How two variables vary together
Statistics 111 - Lecture 7 Exploring Data Numerical Summaries for Relationships between Variables Administrative Notes Homework 1 due in recitation: Friday, Feb. 5 Homework 2 now posted on course website:
More informationPredicting Results of March Madness Using the Probability Self-Consistent Method
International Journal of Sports Science 2015, 5(4): 139-144 DOI: 10.5923/j.sports.20150504.04 Predicting Results of March Madness Using the Probability Self-Consistent Method Gang Shen, Su Hua, Xiao Zhang,
More informationA IMPROVED VOGEL S APPROXIMATIO METHOD FOR THE TRA SPORTATIO PROBLEM. Serdar Korukoğlu 1 and Serkan Ballı 2.
Mathematical and Computational Applications, Vol. 16, No. 2, pp. 370-381, 2011. Association for Scientific Research A IMPROVED VOGEL S APPROXIMATIO METHOD FOR THE TRA SPORTATIO PROBLEM Serdar Korukoğlu
More informationBasketball field goal percentage prediction model research and application based on BP neural network
ISSN : 0974-7435 Volume 10 Issue 4 BTAIJ, 10(4), 2014 [819-823] Basketball field goal percentage prediction model research and application based on BP neural network Jijun Guo Department of Physical Education,
More informationLesson 18: There Is Only One Line Passing Through a Given Point with a Given Slope
There Is Only One Line Passing Through a Given Point with a Given Slope Classwork Opening Exercise Examine each of the graphs and their equations. Identify the coordinates of the point where the line intersects
More informationJournal of Emerging Trends in Computing and Information Sciences
A Study on Methods to Calculate the Coefficient of Variance in Daily Traffic According to the Change in Hourly Traffic Volume Jung-Ah Ha Research Specialist, Korea Institute of Construction Technology,
More informationThe Willingness to Walk of Urban Transportation Passengers (A Case Study of Urban Transportation Passengers in Yogyakarta Indonesia)
The Willingness to Walk of Urban Transportation Passengers (A Case Study of Urban Transportation Passengers in Yogyakarta Indonesia) Imam Basuki 1,a 1 Civil Engineering Program Faculty of Engineering -
More informationAerodynamic Analyses of Horizontal Axis Wind Turbine By Different Blade Airfoil Using Computer Program
ISSN : 2250-3021 Aerodynamic Analyses of Horizontal Axis Wind Turbine By Different Blade Airfoil Using Computer Program ARVIND SINGH RATHORE 1, SIRAJ AHMED 2 1 (Department of Mechanical Engineering Maulana
More informationCoaches, Parents, Players and Fans
P.O. Box 865 * Lancaster, OH 43130 * 740-808-0380 * www.ohioyouthbasketball.com Coaches, Parents, Players and Fans Sunday s Championship Tournament in Boys Grades 5th thru 10/11th will be conducted in
More informationStudy of an Oxygenation Process in Capillary. in the Presence of Magnetic Field
Int. Journal of Math. Analysis, Vol. 4,, no. 35, 697-76 Study of an Oxygenation Process in Capillary in the Presence of Magnetic Field ekha Bali* and Usha Awasthi ** Harcourt Butler Technological Institute,
More informationAnalysis of Variance. Copyright 2014 Pearson Education, Inc.
Analysis of Variance 12-1 Learning Outcomes Outcome 1. Understand the basic logic of analysis of variance. Outcome 2. Perform a hypothesis test for a single-factor design using analysis of variance manually
More informationSTANDARD SCORES AND THE NORMAL DISTRIBUTION
STANDARD SCORES AND THE NORMAL DISTRIBUTION REVIEW 1.MEASURES OF CENTRAL TENDENCY A.MEAN B.MEDIAN C.MODE 2.MEASURES OF DISPERSIONS OR VARIABILITY A.RANGE B.DEVIATION FROM THE MEAN C.VARIANCE D.STANDARD
More informationPSY201: Chapter 5: The Normal Curve and Standard Scores
PSY201: Chapter 5: The Normal Curve and Standard Scores Introduction: Normal curve + a very important distribution in behavior sciences + three principal reasons why... - 1. many of the variables measured
More informationThe final set in a tennis match: four years at Wimbledon 1
Published as: Journal of Applied Statistics, Vol. 26, No. 4, 1999, 461-468. The final set in a tennis match: four years at Wimbledon 1 Jan R. Magnus, CentER, Tilburg University, the Netherlands and Franc
More informationAverage Runs per inning,
Home Team Scoring Advantage in the First Inning Largely Due to Time By David W. Smith Presented June 26, 2015 SABR45, Chicago, Illinois Throughout baseball history, the home team has scored significantly
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(3): Research Article
Available online www.jocpr.com Journal of Chemical and Pharmaceutical Research 2014 6(3):304-309 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 World men sprint event development status research
More informationConfidence Interval Notes Calculating Confidence Intervals
Confidence Interval Notes Calculating Confidence Intervals Calculating One-Population Mean Confidence Intervals for Quantitative Data It is always best to use a computer program to make these calculations,
More informationCommunication Amid Uncertainty
Communication Amid Uncertainty Madhu Sudan Harvard University Based on joint works with Brendan Juba, Oded Goldreich, Adam Kalai, Sanjeev Khanna, Elad Haramaty, Jacob Leshno, Clement Canonne, Venkatesan
More informationAn Empirical Comparison of Regression Analysis Strategies with Discrete Ordinal Variables
Kromrey & Rendina-Gobioff An Empirical Comparison of Regression Analysis Strategies with Discrete Ordinal Variables Jeffrey D. Kromrey Gianna Rendina-Gobioff University of South Florida The Type I error
More informationRobust specification testing in regression: the FRESET test and autocorrelated disturbances
Robust specification testing in regression: the FRESET test and autocorrelated disturbances Linda F. DeBenedictis and David E. A. Giles * Policy and Research Division, Ministry of Human Resources, 614
More informationOptimizing Cyclist Parking in a Closed System
Optimizing Cyclist Parking in a Closed System Letu Qingge, Killian Smith Gianforte School of Computing, Montana State University, Bozeman, MT 59717, USA Abstract. In this paper, we consider the two different
More informationCalculation of Trail Usage from Counter Data
1. Introduction 1 Calculation of Trail Usage from Counter Data 1/17/17 Stephen Martin, Ph.D. Automatic counters are used on trails to measure how many people are using the trail. A fundamental question
More informationEvaluation of step s slope on energy dissipation in stepped spillway
International Journal of Engineering & Technology, 3 (4) (2014) 501-505 Science Publishing Corporation www.sciencepubco.com/index.php/ijet doi: 10.14419/ijet.v3i4.3561 Research Paper Evaluation of step
More informationAbstract In this paper, the author deals with the properties of circumscribed ellipses of convex quadrilaterals, using tools of parallel projective tr
Study on the Properties of Circumscribed Ellipses of Convex Quadrilaterals Author: Yixi Shen Mentors: Zhongyuan Dai; Yijun Yao No. High School of East China Normal University Shanghai, China December,
More informationMeasuring Returns to Scale in Nineteenth-Century French Industry Technical Appendix
Measuring Returns to Scale in Nineteenth-Century French Industry Technical Appendix Ulrich Doraszelski Hoover Institution, Stanford University March 2004 Formal Derivations Gross-output vs value-added
More informationAssignment. To New Heights! Variance in Subjective and Random Samples. Use the table to answer Questions 2 through 7.
Assignment Assignment for Lesson.1 Name Date To New Heights! Variance in Subjective and Random Samples 1. Suppose that you have collected data for the weights of all of the crates in a warehouse. a. Give
More informationEfficiency Wages in Major League Baseball Starting. Pitchers Greg Madonia
Efficiency Wages in Major League Baseball Starting Pitchers 1998-2001 Greg Madonia Statement of Problem Free agency has existed in Major League Baseball (MLB) since 1974. This is a mechanism that allows
More informationValidation Study of Gas Solubility Correlations at bubble point pressure for Some Libyan Crude Oils Using Three chosen Correlations
Validation Study of Gas Solubility Correlations at bubble point pressure for Some Libyan Crude Oils Using Three chosen Correlations Dr. Mustafa O. Sharrad Dept. of Chemical and Petroleum Engineering, Faculty
More informationCommunication Amid Uncertainty
Communication Amid Uncertainty Madhu Sudan Harvard University Based on joint works with Brendan Juba, Oded Goldreich, Adam Kalai, Sanjeev Khanna, Elad Haramaty, Jacob Leshno, Clement Canonne, Venkatesan
More informationConservation of Energy. Chapter 7 of Essential University Physics, Richard Wolfson, 3 rd Edition
Conservation of Energy Chapter 7 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Different Types of Force, regarding the Work they do. gravity friction 2 Conservative Forces BB WW cccccccc
More informationGENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2
GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2 S. T. Buttram 3, R. L. Willham 4 and D. E. Wilson 4 Iowa State University, Ames 50011 ABSTRACT
More informationCorrelation analysis between UK onshore and offshore wind speeds
Loughborough University Institutional Repository Correlation analysis between UK onshore and offshore wind speeds This item was submitted to Loughborough University's Institutional Repository by the/an
More informationWeek 7 One-way ANOVA
Week 7 One-way ANOVA Objectives By the end of this lecture, you should be able to: Understand the shortcomings of comparing multiple means as pairs of hypotheses. Understand the steps of the ANOVA method
More informationsave percentages? (Name) (University)
1 IB Maths Essay: What is the correlation between the height of football players and their save percentages? (Name) (University) Table of Contents Raw Data for Analysis...3 Table 1: Raw Data...3 Rationale
More informationPractical Approach to Evacuation Planning Via Network Flow and Deep Learning
Practical Approach to Evacuation Planning Via Network Flow and Deep Learning Akira Tanaka Nozomi Hata Nariaki Tateiwa Katsuki Fujisawa Graduate School of Mathematics, Kyushu University Institute of Mathematics
More informationEffect of body measurements on first lactation length in Jersey crosses and Holstein Friesian crosses
IOSR Journal of Agriculture and Veterinary Science (IOSR-JAVS) e-issn: 2319-2, p-issn: 2319-2372. Volume 10, Issue 7 Ver. II (July 2017), PP 71-76 www.iosrjournals.org Effect of body measurements on first
More informationExperimental Determination of Temperature and Pressure Profile of Oil Film of Elliptical Journal Bearing
International Journal of Advanced Mechanical Engineering. ISSN 2250-3234 Volume 4, Number 5 (2014), pp. 469-474 Research India Publications http://www.ripublication.com Experimental Determination of Temperature
More informationDNS Study on Three Vortex Identification Methods
Γ DNS Study on Three Vortex Identification Methods Yinlin Dong Yong Yang Chaoqun Liu Technical Report 2016-07 http://www.uta.edu/math/preprint/ DNS Study on Three Vortex Identification Methods Yinlin Dong
More informationWomen and Marathons: A Low Participation. Recreation Research Proposal. PRM 447 Research and Evaluation in PRM. Jaimie Coastman.
Running WOMEN head: AND WOMEN MARATHONS: AND MARATHONS: A LOW PARTICIPATION A LOW 1 PARTICIPATION Women and Marathons: A Low Participation Recreation Research Proposal PRM 447 Research and Evaluation in
More informationEE582 Physical Design Automation of VLSI Circuits and Systems
EE Prof. Dae Hyun Kim School of Electrical Engineering and Computer Science Washington State University Routing Grid Routing Grid Routing Grid Routing Grid Routing Grid Routing Lee s algorithm (Maze routing)
More informationWhich On-Base Percentage Shows. the Highest True Ability of a. Baseball Player?
Which On-Base Percentage Shows the Highest True Ability of a Baseball Player? January 31, 2018 Abstract This paper looks at the true on-base ability of a baseball player given their on-base percentage.
More information