In his seminal book, Shewhart (1931) makes no demand on the distribution of the characteristic to be plotted on a control chart. How then can we explain the idea that normality is, if not required, at least highly desirable? I believe that it has come about through the many statistical studies of control-chart behavior. If one is to study how a control chart behaves, it is necessary to relate it to some distribution. The obvious choice is the normal distribution because of its ubiquity as a satisfactory model. This is bolstered by the existence of the Central Limit Theorem.

Sampling: Design and Analysis

Pandurang V. Sukhatme: Sampling Theory of Surveys with Applications. Food and Agriculture Organisation of United Nations. Iowa State College Press and Indian Society of Agricultural Statistics. 1954. Pp. xxxi + 491. Rs. 25 or US $5.50.

Sampling Theory of Surveys with Applications

A general family of estimators, which use the information of two auxiliary variables in the stratified random sampling, is proposed to estimate the population mean of the variable under study. Under stratified random sampling without replacement scheme, the expressions of bias and mean square error (MSE) up to the first- and second-order approximations are derived. The family of estimators in its optimum case is discussed. Also, an empirical study is carried out to show the properties of the proposed estimators.

Family of Estimators of Population Mean Using Two Auxiliary Variables in Stratified Random Sampling

This paper addresses the problem of estimating the population mean of the study variate Y using information on two auxiliary variables X 1 and X 2 . A ratio-cum-product type exponential estimator has been suggested and its bias and mean squared error have been derived under large sample approximation. An almost unbiased ratio-cum-product type exponential estimator has also been derived by using Jackknife technique envisaged by Quenouille (1956). A generalized version of the ratio-cum-product exponential estimator has also been given along with its properties. Numerical illustration is given in support of the present study.

/pdf/ratio-cum-product-type-exponential-estimator-4i1kz7behx.pdf

Ratio-cum-product type exponential estimator

This paper presents exponential ratio and product estimators for estimating finite population mean using auxiliary information in double sampling and analyzes their properties. These estimators are compared for their precision with simple mean per unit, usual double sampling ratio and product estimators. An empirical study is also carried out to judge the merits of the suggested estimators.

/pdf/modified-exponential-ratio-and-product-estimators-for-finite-3zsohyib5f.pdf

Modified Exponential Ratio and Product Estimators for Finite Population Mean in Double Sampling

This paper proposes a modified ratio-cum-product estimator of finite population mean of the study variate Y using known correlation coefficient between two auxiliary characters X1 and X2. An almost unbiased ratio-cum-product estimator has also been obtained by using Jackknife technique envisaged by Quenouille (1956). The merits of the proposed estimator are examined through a numerical illustration.

/pdf/estimation-of-finite-population-mean-using-known-correlation-eqhnfpf01t.pdf

Estimation of finite population mean using known correlation coefficient between auxiliary characters

This paper proposes a ratio-cum-product estimator of finite population mean using information on coefficient of variation and coefficient of kurtosis of auxiliary variate. The bias and mean squared error of the proposed estimator are obtained. It has been shown that the proposed estimator is more efficient than the sample mean estimator, usual ratio and product estimators and estimators proposed by Upadhyaya and Singh (1999) under certain given conditions. An empirical study is also carried out to demonstrate the merits of the proposed estimator over other estimators.

A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis

In this paper we have suggested two modified estimators of population mean using power transformation. It has been shown that the modified estimators are more efficient than the sample mean estimator, usual ratio estimator, Sisodia and Dwivedi’s (1981) estimator and Upadhyaya and Singh’s (1999) estimator at their optimum conditions. Empirical illustrations are also given for examining the merits of the proposed estimators. Following Kadilar and Cingi (2003) the work has been extended to stratified random sampling, and the same data set has been studied to examine the performance in stratified random sampling.

http://cda.mrs.umn.edu/~jongmink/research/sp2008.pdf

A modified estimator of population mean using power transformation

This paper proposes a ratio-cum-dual to ratio estimator of finite population mean. The bias and mean squared error of the proposed estimator are obtained. It has been shown that the proposed estimator is more efficient than the simple mean estimator, usual ratio estimator and dual to ratio estimator under certain given conditions. An Asymptotic optimum estimator in the class of estimator is identified with its mean squared error formula. To judge the merits of the proposed estimator over other estimators an empirical study is carried out.

/pdf/a-new-ratio-cum-dual-to-ratio-estimator-of-finite-population-25epxmoxho.pdf

Rajesh Tailor

Papers

Ratio-cum-product type exponential estimator

Estimation of finite population mean using known correlation coefficient between auxiliary characters

A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis

A modified estimator of population mean using power transformation

A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling