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In this work, we study the properties of the cumulative residual entropy generating function (CREGF). We also discuss the non parametric estimation of CREGF. We introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely. We study some characterization results using the relationship between DCREGF, hazard rate, and mean residual life function. A new class of life distributions based on decreasing DCREGF is introduced. Finally, we develop a test for decreasing DCREGF and study its performance. [ABSTRACT FROM AUTHOR]

In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative past extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would facilitate finding estimators of these measures. [ABSTRACT FROM AUTHOR]

We propose nonparametric tests for testing mean residual life and mean past life ordering. Asymptotic properties of the proposed test statistics are studied. We also propose Jackknife Empirical Likelihood (JEL) ratio tests for testing mean residual life and mean past life ordering. Some numerical results are presented to evaluate the performance of the proposed tests by comparing them with few competing tests available in the literature. Finally, we illustrate the proposed test procedures using real data sets. [ABSTRACT FROM AUTHOR]

In the present paper, we develop a new goodness of fit test for gamma distribution based on the fixed point characterization. We use U-Statistics theory to derive the test statistic. We discuss how the right censored observations are incorporated into the proposed test. The asymptotic properties of the test statistics in censored and uncensored cases are studied. We carry out a Monte Carlo simulation study to validate the finite sample performance of the proposed tests. We also illustrate the test procedures using real data sets. [ABSTRACT FROM AUTHOR]

Competing risks data with discrete lifetime come up in practice. However, only limited literature exists for such data. In this paper, we propose a non-parametric test based on U-statistics for testing independence of time to failure and cause of failure of competing risks data when the lifetime is a discrete random variable. Asymptotic distribution of the proposed test statistic is derived. An extensive Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed test. The flexibility of the testing procedure is illustrated using real data sets on oral cancer patients and drug-exposed pregnancies. [ABSTRACT FROM AUTHOR]

The widely used income inequality measure, Gini index, is extended to form a family of income inequality measures known as Single-Series Gini (S-Gini) indies. In this study, we develop empirical likelihood (EL) and jackknife empirical likelihood (JEL) based inference for the S-Gini indices. We prove that the limiting distribution of both EL and JEL ratio statistics are Chi-square distributions with one degree of freedom. Using the asymptotic distribution we construct EL and JEL based confidence intervals for relative S-Gini indices. We also give bootstrap-t and bootstrap calibrated empirical likelihood confidence intervals for the S-Gini indices. A numerical study is carried out to compare the performances of the proposed asymptotic confidence interval and the bootstrap methods. A test for S-Gini indices based on jackknife empirical likelihood ratio is also proposed. Finally, we illustrate the proposed method using an income data. [ABSTRACT FROM AUTHOR]

In this article, we propose a family of non-parametric tests for testing exponentiality against decreasing mean time to failure class alternatives. We obtain the exact null distribution of the test statistic and calculate the critical values for different sample sizes. We also extend our test to incorporate right censored observations. We discuss the efficiency loss due to censoring and calculate it for some choice of censoring distribution. A simulation result is presented to show the performance of the proposed test. Finally, the test procedure is illustrated using a real data. [ABSTRACT FROM AUTHOR]

Based on U-empirical process we construct a jackknife empirical likelihood-based test for testing one-sided Lévy distribution. Adjusted jackknife empirical likelihood test also developed. The simulation study shows that the proposed tests have very good power for various alternatives. Finally, we illustrate the test procedure using three real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalized moment identity for the case when the distributions of the random variables are not necessarily purely discrete or absolutely continuous. The proposed identity is useful to find the generator which has been used for the approximation of distributions by Stein's method. Apparently, a new approach is discussed for the approximation of distributions by Stein's method. We bring the characterization based on the relationship between conditional expectations and hazard measure in our unified framework. As an application, a new lower bound to the mean-squared error is obtained and it is compared with Bayesian Cramer-Rao bound. [ABSTRACT FROM AUTHOR]

The Gini methodology in statistical inference and related area has got much attention in recent years. In this paper, using a characterisation based on the Gini index we develop a nonparametric test for testing exponentiality against new better than used in expectation class. We derive the exact null distribution of the proposed test statistic and then calculate the critical values for different sample sizes. Asymptotic properties of the test statistic are discussed. The test is compared with some other test by evaluating Pitman's asymptotic efficacy. We also discuss how to incorporate right-censored observations in our study. A simulation study is presented to demonstrate the performance of the testing method. Finally, we illustrated our test procedure using two real data sets. [ABSTRACT FROM AUTHOR]

Abstract Tests for the goodness of fit of logistic distribution have received much attention in the literature as it is widely used in many studies related to bio-assay, population growth, etc. In this paper, we propose a method to test whether the data comes from a logistic distribution or not. We derive the asymptotic distribution of the test statistic. Also, we develop a test based on Jackknife Empirical Likelihood (JEL). The finite sample performance of the JEL ratio test is evaluated through Monte Carlo simulation. We illustrate the proposed method using a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we develop an exact test for testing exponentiality against renewal increasing mean residual life class. The critical values are presented for different sample sizes. Asymptotic properties of the test statistic are also studied. Some numerical results are presented for evaluating the performance of the proposed test. The test procedure is illustrated by using two real data sets. The proposed method is then modified to incorporate right censored observations and the efficiency loss due to censoring is evaluated using Pitman's asymptotic efficacy value. [ABSTRACT FROM AUTHOR]