20 research outputs found
ON TESTING AGAINST POSITIVE QUADRANT DEPENDENCE BASED ON SUB-SAMPLE ORDER STATISTICS
No full textA 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
Selection of the Best New Better than used Population Based on Subsamples
No full textThe 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
A CLASS OF DISTRIBUTION-FREE TESTS FOR INDEPENDENCE AGAINST POSITIVE QUADRANT DEPENDENCE
No full textA 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
Reliability Estimation in Multicomponent Stress-Strength Model Based on Generalized Pareto Distribution
No full textThe paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X1, X2, … Xk being independently and identically distributed random variables and each component is experiencing a random stress Y. The s-out-of-k system is said to function if atleast s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The reliability of such a system is derived when both strength and stress variables follow generalized Pareto distribution. The system reliability is estimated using maximum likelihood and Bayesian approaches. The maximum likelihood estimators are derived under both simple random sampling and ranked set sampling schemes. Lindley's approximation technique is used to get approximate Bayes estimators. The reliability estimators obtained from both the methods are compared by using mean squares error criteria and real data analysis is carried out to illustrate the procedure
On Distribution Free Tests for the Two-Sample Location Problem Based on Signs of Extreme Observations
No full textA 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
ON DISTRIBUTION FREE TESTS FOR THE TWO-SAMPLE LOCATION PROBLEM BASED ON SIGNS OF EXTREME OBSERVATIONS
No full textA 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
Estimation of Stress Strength Reliability for Transmuted Exponentiated Inverse Rayleigh Distribution
No full textThe 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
Rank Tests for Independence Against Weighted Alternative with Missing Values
No full textOne 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
On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions
No full textA Class of Nonparametric Tests for the Two-Sample Location Problem
No full textThe 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
