Search

The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function (WCREGF) and study its properties. We then introduce the dynamic weighted cumulative residual entropy generating function (DWCREGF). It is shown that the DWCREGF determines the distribution uniquely. We study some characterization results using the relationship between the DWCREGF and the hazard rate and/or the mean residual life function. Using a characterization based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the proposed test. Finally, the test is illustrated using two real data sets., Comment: arXiv admin note: text overlap with arXiv:2211.05484

In this work, we study the properties of cumulative residual entropy generating function. We then 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 and hazard rate and mean residual life function. A new class of life distribution based on decreasing DCREGF is introduced. Finally we develop a test for decreasing DCREGF and study its performance.

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 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 enable us to find estimators of these measures.

We develop a new goodness fit test for Rayleigh distribution for complete as well as right censored data. We use U-Statistic theory to derive the test statistic. First we develop a test for complete data and then discuss, how right censored observations can be incorporated in the testing procedure. The asymptotic properties of the test statistics in both uncensored and censored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We illustrate the procedures using real data sets. We also provide, a goodness of fit test for standard Rayleigh distribution based on jackknife empirical likelihood., Comment: arXiv admin note: substantial text overlap with arXiv:2108.00503

In the present article, we propose jackknife empirical likelihood (JEL) ratio test for testing the independence of time to failure and cause of failure in competing risks data. We use U-statistic theory to derive the JEL ratio test. The asymptotic distribution of the test statistic is shown to be chi-square distribution with one degree of freedom. A Monte Carlo simulation study is carried out to assess the finite sample behaviour of the proposed test. The performance of proposed JEL test is compared with the test given in Dewan et al. (2004). Finally we illustrate our test procedure using various real data sets.

Panel count data refer to the data arising from studies concerning recurrent events where study subjects are observed only at distinct time points. If these study subjects are exposed to recurrent events of several types, we obtain panel count data with multiple modes of recurrence. In the present paper, we propose a nonparametric test for comparing cause specific rate functions of panel count data with more than one mode of recurrence. The test can also be employed to assess whether the competing modes of recurrence are affecting the recurrence times identically. We carry out simulation studies to evaluate the performance of the test statistic in a finite sample setup. The proposed test is illustrated using two real life panel count data sets, one arising from a medical follow up study on skin cancer chemo prevention trial and the other on a warranty database for a fleet of automobiles., Comment: arXiv admin note: substantial text overlap with arXiv:2106.01636

Extropy and its properties are explored to quantify the uncertainty. In this paper, we obtain alternative expressions for cumulative residual extropy and negative cumulative extropy. We obtain simple estimators of cumulative (residual) extropy. Asymptotic properties of the proposed estimators are studied. We also present new estimators of cumulative (residual) extropy when the data is right censored. The finite sample performance of the estimators is evaluated through Monte Carlo simulation studies. We use the proposed estimators to analyse different real data sets. Finally, we obtain the relationship between different dynamic and weighted extropy measures and reliability concepts, which leads to several open problems associated with these measures., Comment: We obtain the relationship between different dynamic and weighted extropy measures and reliability concepts. These lead to several open problems associated with dynamic and weighted extropy measures

In the present paper, we develop a new goodness fit test for gamma distribution using the fixed point characterization. U-Statistic theory is employed to derive the test statistic. We discuss how the right censored observations are incorporated in the test developed here. The asymptotic properties of the test statistic in both censored and uncensored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We also illustrate the test procedure using several real data sets., Comment: This is the first test for gamma distribution which address right censoring

Panel count data is common when the study subjects are exposed to recurrent events, observed only at discrete time points. In this article, we consider the regression analysis of panel count data with multiple modes of recurrence. We propose a proportional mean model to estimate the effect of covariates on the underlying counting process due to different modes of recurrence. The simultaneous estimation of baseline cumulative mean functions and regression parameters of $(k>1)$ recurrence modes are studied in detail. Asymptotic properties of the proposed estimators are also established. A Monte Carlo simulation study is carried out to validate the finite sample behaviour of the proposed estimators. The methods are applied to a real data arising from skin cancer chemoprevention trial., Comment: 25 pages, 2 fgires

Using fixed point characterization, we develop a new goodness of fit test for uniform distribution. We also discuss how the right censored observations can be incorporated in the proposed test procedure. We study the asymptotic properties of the proposed test statistics. A Monte Carlo simulation is carried out to evaluate the finite sample performance of the tests. We illustrate the test procedures using real data sets.

Panel count data arise from longitudinal studies on recurrent events where each subject is observed only at discrete time points. If recurrent events of several types are possible, we obtain panel count data with multiple modes of recurrence. Such data is commonly encountered in medical studies, reliability experiments as well as in sociological studies. In this article, we present cause specific rate functions for the analysis of panel count data with multiple modes of recurrence and develop nonparametric estimation procedures for the same. We derive empirical estimators for the cause specific rate functions and also propose a smoothed version of the same estimators using kernel estimation method. Asymptotic properties of the proposed estimators are studied. A simulation study is conducted to assess the performance of the proposed estimators in finite samples. The practical utility of the proposed method is demonstrated using a real life data arising from skin cancer chemoprevention trial given in Sun and Zhao (2013).

Competing risks data with discrete lifetime comes 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.

We propose a new method for the analysis of competing risks data with long term survivors. The proposed method enables us to estimate the overall survival probability and cure fraction simultaneously. We formulate the effect of covariates on cumulative incidence functions using linear transformation models. Estimating equations based on counting process are developed to estimate regression coefficients. The asymptotic properties of the estimators are studied using martingale theory. An extensive Monte Carlo simulation study is carried out to assess the finite sample performance of the proposed estimators. Finally, we illustrate our method using a real data set., Comment: We propose a new methodology in mixture cure rate model with competing risks data