The power functions of the likelihood ratio tests for a simple tree ordering in normal means: unequal weights

Likelihood ratio tests are considered for two testing situations; testing for the homogeneity of k normal means against the alternative restricted by a simple tree ordering trend and testing the null hypothesis that the means satisfy the trend against all alternatives. Exact expressions are given for the power functions for k = 3 and 4 and unequal sample sizes, both for the case of known and unknown population variances, and approximations are discussed for larger k. Also, Bartholomew’s conjectures concerning minimal and maximal powers are investigated for the case of equal and unequal sample sizes. The power formulas are used to compute powers for a numerical example.     

Generalized franklin's model for randomized response sampling

In this paper we introduce two estimators of a population proportion when randomized response sampling with a normal randomizing distribution is used* The estimators have been obtained by using the method of moments. Both of the proposed estimators are shown to be more efficient than the corresponding estimators of Eranklin (1989 b).     

A test for exponentiatity against hnbue alternatives

Neyman's asymptotically most powerful test in the class of al1 similar tests for testing exponentiality against a parametric class of Makeham alternatives is shown to be consistent for the much wider class of harmonic new better than used in expectation distributions.     

Some Imputation Methods to Minimize the Effect of Non Response in Two-Occasion Rotation Patterns

Among modern strategies applied to cope with non response, a major problem faced by survey statisticians, imputation is one of the most common. Imputation is the filling up method of incomplete data for adapting the standard analytic model in statistics. The purpose of the present work is to study the use of imputation methods in dealing with non response which occur at both occasions in two-occasion successive (rotation) sampling. Chain-type regressions in ratio estimators have been proposed for estimating the population mean at current occasion. Expressions for optimum estimator and its mean square error have been derived. To study the effectiveness of the imputation methods, performances of the proposed estimators are compared in two different situations: with and without non response. Behavior of the proposed estimators is demonstrated through empirical studies.     

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982 Chen , H. J. ( 1982 ). A new range statistic for comparisons of several exponential location parameters . Biometrika 69 ( 1 ): 257 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) and of Dhawan and Gill (1999 Dhawan , A. K. , Gill , A. N. ( 1999 ). A one-sided test for testing homogeneity of scale parameters against ordered alternative . Communication in Statistics—Theory and Methods 28 ( 10 ): 2417 – 2439 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is carried out using Monte-Carlo simulation.     

A Tutorial of Survival Modeling to Capture Covariate Effect

Mixture modeling in general and expectation–maximization in particular are too cumbersome and confusing for applied health researchers. Consequently, the full potential of mixture modeling is not realized. To remedy the deficiency, this tutorial article is prepared. This article addresses important applied problems in survival analysis and handles them in deeper generality than the existing work, especially from the point of view of taking covariates into account. In specific, the article demonstrates the concepts, tools, and inferencial procedure of mixture modeling using head-and-neck cancer data and survival time after heart transplant surgery data.     

Efficient Ratio and Product Estimators in Stratified Random Sampling

This paper suggests an efficient class of ratio and product estimators for estimating the population mean in stratified random sampling using auxiliary information. It is interesting to mention that, in addition to many, Koyuncu and Kadilar (2009 Koyuncu , N. , Kadilar , C. ( 2009 ). Ratio and product estimators in stratified random sampling . J. Statist. Plann. Infer. 139 : 2552 – 2558 .[Crossref], [Web of Science ®] , [Google Scholar]), Kadilar and Cingi (2003 Kadilar , C. , Cingi , H. ( 2003 ). Ratio estimator in stratified sampling . Biometr. J. 45 : 218 – 225 .[Crossref], [Web of Science ®] , [Google Scholar], 2005 Kadilar , C. , Cingi , H. ( 2005 ). A new estimator in stratified random sampling . Commun. Statist. Theor. Meth. 34 : 597 – 602 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Singh and Vishwakarma (2007 Singh , H. P. , Vishwakarma , G. K. ( 2007 ). Modified exponential ratio and product estimators for finite population mean in double sampling . Austr. J. Statist. 36 ( 3 ): 217 – 225 . [Google Scholar]) estimators are identified as members of the proposed class of estimators. The expressions of bias and mean square error (MSE) of the proposed estimators are derived under large sample approximation in general form. Asymptotically optimum estimator (AOE) in the class is identified alongwith its MSE formula. It has been shown that the proposed class of estimators is more efficient than combined regression estimator and Koyuncu and Kadilar (2009 Koyuncu , N. , Kadilar , C. ( 2009 ). Ratio and product estimators in stratified random sampling . J. Statist. Plann. Infer. 139 : 2552 – 2558 .[Crossref], [Web of Science ®] , [Google Scholar]) estimator. Moreover, theoretical findings are supported through a numerical example.     

Improved estimation of scale parameters of morgenstern type bivariate uniform distribution using ranked set sampling

ABSTRACT

In this article we suggest some improved version of estimators of scale parameter of Morgenstern-type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X, Y) follows a MTBUD. We also suggest some linear shrinkage estimators of scale parameter of Morgenstern type bivariate uniform distribution (MTBUD). Efficiency comparisons are also made in this work.