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In this paper, we propose the Bayes estimators of unknown parameters of power function distribution in the context of double censoring. The maximum-likelihood estimators (MLEs) for the power function parameters are derived. Bayes estimators are derived using the squared error loss function, entropy loss function, and linex loss function using the Lindley approximation and the importance sampling procedures. We also introduced sample prediction estimates using Bayesian techniques. Finally, we perform a simulation study to compare all the proposed estimation methods and analyze a real-life data set for illustration purposes. [ABSTRACT FROM AUTHOR]

The present study focus on the ordered approach of random variables in the analysis of uncertainty using cumulative extropy and its dynamic versions. Some important results regarding bounds, aging properties and orderings of cumulative extropy measures based on order statistics have been discussed. The study also presents characterizations of some probability distribution, identical distribution of random variables and symmetry of a probability distribution using cumulative extropy measures based on extreme order statistics. Further, a simple empirical estimator has been proposed to estimate dynamic failure extropy using a real life data set. [ABSTRACT FROM AUTHOR]

In certain applied areas such as reliability and mathematical neurobiology, it is often required to deal with shift-dependent measures of uncertainty. In this paper, we propose a shift-dependent uncertainty measure related to extropy that assigns higher weight to larger values of the random variable. Moreover, in order to describe the dynamic information of random lifetimes, we consider weighted dynamic survival and failure extropies along with some of its properties as well. Further, we have also established nonparametric estimators for the proposed measures. The methods are illustrated using simulated and real data sets. [ABSTRACT FROM AUTHOR]

In this work, the residual extropy for measuring uncertainty involved in the remaining lifetime of a component has been investigated based on records. Some intriguing properties based on residual extropy of records have been discussed. The study also proposes a simple estimator for residual extropy of records and the performance of the proposed estimator has been evaluated as well. A detailed discussion about the betterness of using records over the random sample for estimating residual extropy has been presented based on a real life data set. [ABSTRACT FROM AUTHOR]

This study proposes a new test for testing the symmetry in the distribution of the data observed on a random variable. The test for symmetry has been constructed using a characterization result derived based on the extropy of k-records. The empirical density and critical values of the newly proposed test statistic have been obtained in this work. This study also analyses the performance of the test statistic based on the power values computed using Monte Carlo simulation methods and a comparison study with 10 competitor tests has been carried out. Moreover, the test procedure has been implemented on four real-life data sets to verify its performance in identifying the symmetric nature. [ABSTRACT FROM AUTHOR]

In the present article, we propose nonparametric estimators for the past inaccuracy measure for the lifetime distribution based on right censored data. Two non parametric estimators, one based on the empirical distribution function and the other using kernel density estimator, are proposed. Asymptotic properties of the estimators are established under suitable regularity conditions. Monte-Carlo simulation studies are carried out to compare the performance of the estimators. The method is illustrated using a real data set. [ABSTRACT FROM AUTHOR]

Recently, Lad et al. proposed an alternative measure of uncertainty of a random variable called extropy. In this paper, we propose a new measure called survival extropy and study some of its properties. We have also considered the dynamic form of the survival extropy. Properties and characterization of the new measures are discussed. Moreover, we obtain non parametric estimators for the proposed measure. Monte Carlo simulation study and illustration using real data set are done to verify the performance of the estimators. [ABSTRACT FROM AUTHOR]

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates. [ABSTRACT FROM AUTHOR]

In the present paper, we propose non parametric estimators for the inaccuracy measure for the lifetime distribution based on censored data. This measure plays important roles in reliability and survival analysis in connection with modeling and analysis of life time data. Asymptotic properties of the estimators are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to compare the performance of the estimators using the mean-squared error. The methods are illustrated using a real data set. [ABSTRACT FROM AUTHOR]

Recently, Abbasnejad et al. (2010) proposed a measure of uncertainty based on survival function, called the survival entropy of order α. A dynamic form of the survival entropy of order α is also proposed by them. In this paper, we derive the weighted form of these measures. The properties of the new measures are also discussed. [ABSTRACT FROM AUTHOR]