On Distribution Free Tests for the Two-Sample Location Problem Based on Signs of Extreme Observations

A class of distribution-free tests for two-sample location problem is based on the signs of most extreme observations in the sub-samples of sizes c and d from X and Y samples respectively. The test statistics have been expressed in terms of linear rank statistics. The asymptotic normality of the test statistics is established. Asymptotic efficiencies indicate that members of our class do well in comparison with some already existing test statistics for light and medium tailed distributions

Selection of the Best New Better than used Population Based on Subsamples

The present study considers the problem of selecting the ‘Best’ new better than used(NBU) population among the several NBU populations. The procedure to select the ‘Best’ NBU population is developed based on a measure of departure from exponentiality towards NBU, proposed by Pandit and Math(2009)for the problem of testing exponentiality against NBU alternatives in one sample setting. The selection procedure is based on large sample properties of the statistic proposed in Pandit and Math(2009).We also indicate some applications of the selection procedur

Rank Tests for Independence Against Weighted Alternative with Missing Values

One of the common problems of practical importance is that of determining whether there is independence between a pair of random variables. In this paper, the problem of testing independence of bivariate random variables against a weighted alternative model with possible missing values on both responses is considered. The model considered here is due to Shei, Bai and Tsai [9] which is the generalization of Hajek and Sidak [12] model with weighted contamination. A new rank test based on ranks is proposed and its asymptotic normality is established. Locally most powerful tests for the model is derived. The asymptotic null distributions of the test statistics are also provided for the purpose of practical us

Estimation of Stress Strength Reliability for Transmuted Exponentiated Inverse Rayleigh Distribution

The problem of estimation of reliability of systems in stress-strength set up is an important area of research in Statistics, particularly, in Statistical Inference on reliability. In this paper, the estimation of stress-strength reliability when the strength and stress variables are assumed to be independently distributed as transmuted exponentiated inverse Rayleigh distribution (TEIRD) is considered. The TEIRD is a general distribution which includes transmuted inverse Rayleigh distribution, exponentiated inverse Rayleigh distribution and inverse Rayleigh distribution as a particular cases. The maximum likelihood estimator of stress -strength model is derived. Also, asymptotic confidence interval for reliability is constructed. The real data analysis is considered and the simulation study is conducted

ON DISTRIBUTION FREE TESTS FOR THE TWO-SAMPLE LOCATION PROBLEM BASED ON SIGNS OF EXTREME OBSERVATIONS

A class of distribution-free tests for two-sample location problem is based on the signs of most extreme observations in the sub-samples of sizes c and d from X and Y samples respectively. The test statistics have been expressed in terms of linear rank statistics. The asymptotic normality of the test statistics is established. Asymptotic e�ciencies indicate that members of our class do well in comparison with some already existing test statistics for light and medium tailed distribution

ON TESTING AGAINST POSITIVE QUADRANT DEPENDENCE BASED ON SUB-SAMPLE ORDER STATISTICS

A new class of tests based on convex combination of the two statistics is proposed. These are functions of sub-sample order statistics. The classes of tests proposed by Kochar and Gupta [6], Shetty and Pandit [16], Pandit and Kumari [11] and Kendall’s test lie in the proposed class of test statistics. The asymptotic normality of the proposed class of tests is established. It has been observed that some members of the class perform better than the existing tests. Unbiasedness and consistency of the proposed class of tests are established

System Reliability Estimation in Multicomponent Exponential-Lindley Stress-Strength Models

A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths ( ) 1 2 , ,..., k X X X are subjected to one of the r random stresses ( ) 1 2 , ,..., r Y Y Y . The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow Lindley distribution and Exponential distribution respectively. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimators

SOME CLASSES OF NONPARAMETRIC TESTS FOR SPECIAL TWO-SAMPLE LOCATION PROBLEM BASED ON SUBSAMPLE EXTREMES

The special two-sample location problem is an important problem which is useful in comparing the performance of two measuring instruments. The problem of comparing the performances of two packing machines in which one machine may underfill the packets and the other may overfill the packets on an average, fits into special twosample location setup wherein one wishes to test for the point of symmetry versus an appropriate alternative. The only test available in the literature to the best of our knowledge is the class of tests due to Shetty and Umarani [13] which is based on U-statistics. In this paper, two classes of test statistics are proposed which are based on extremes of subsamples. The performances of the proposed classes of tests ar

A Class of Nonparametric Tests for the Two-Sample Location Problem

The two-sample location problem is one of the fundamental problems encountered in Statistics. In many applications of Statistics, two-sample problems arise in such a way as to lead naturally to the formulations of the null hypothesis to the effect that the two samples come from identical populations. A class of nonparametric test statistics is proposed for two-sample location problem based on U-statistic with the kernel depending on a constant ’a’ when the underlying distribution is symmetric. The optimal choice of ’a’ for different underlying distributions is determined. An alternative expression for the class of test statistics is established. Pitman asymptotic relative efficiencies indicate that the proposed class of test statistics does well in comparison with many of the test statistics available in the literature. The small sample performance is also studied through Monte-Carlo Simulation techniqu

Tests for Two-Sample Location Problem Based on Subsample Quantiles

This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distribution