21 research outputs found
A CLASS OF DISTRIBUTION-FREE TESTS FOR INDEPENDENCE AGAINST POSITIVE QUADRANT DEPENDENCE
<p class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-size: 12.0pt; font-family: "Times New Roman","serif";" lang="EN-IN">A class of distribution-free tests based on convex combination of two U-statistics is considered for testing independence against positive quadrant dependence. The class of tests proposed by Kochar and Gupta (1987) and Kendall’s test are members of the proposed class. The performance of the proposed class is evaluated in terms of Pitman asymptotic relative efficiency for Block- Basu (1974) model and Woodworth family of distributions. It has been observed that some members of the class perform better than the existing tests in the literature. Unbiasedness and consistency of the proposed class of tests have been established.</span></p
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