In this present work, we are going to show the various useful properties of the existing distribution known as MG(Exp)(epsilon)-distribution which have not quoted by the host authors like moments, mean deviation about mean, mean deviation about median, order statistics, count of uncertainty. Estimation procedures have been adopted under Bayesian estimation for progressive Type-II censored case. Simulation study has also been carried out to judge the behavior of the Bayes estimator at the long-run. Performance of the Bayes estimators and their posterior risks of the considered loss functions have been obtained, reported and compared for the considered values of sample size, effective sample size, parameter and removals. The comparison of Bayes estimators of all 6 chosen loss functions have been done on the ground of lowest posterior risks.

The objective of the paper is to initiate a new extension of inverse Lomax distribution represented by transmuted inverse Lomax distribution (TILD). The quadratic rank transmutation map (QRTM) method has been used to generate this probability distribution by inserting new parameter that would lead more flexibility. Different statistical properties like moments, inverse moments, moment generating function, quantile function, order statistics etc. have been discussed. Maximum likelihood method of estimation has been discussed and used to estimate the unknown parameter of the proposed model. A real data set has also been carried out to know the usefulness of the model in real life scenario and compared with some chosen distributions on the basis of some chosen model selection criterions.

In statistical literature, several methods are available to generate a new probability distribution by introducing new parameter to any existing standard distribution.The quadratic rank transmutation map method is one of these and received considerable attention in the literature.Here, we also proposed a new probability distribution using this method when DUSE(θ)distribution is chosen as baseline distribution.The proposed distribution is called transmuted DUSE(θ)-distribution, which is seems to be more flexible as compared to the baseline distribution.Different statistical properties such as moments, quantile function, survival function, hazard function and order statistics have been derived.Also, the method of maximum likelihood and method of maximum product spacing are used to estimate the unknown parameters of the introduced probability distribution.Simulation study is being carried out to know the long-run behavior of the distribution.Finally, a real data set has been utilized to show the applicability of the proposed distribution.

A new asymmetric loss function which is suitable for estimation of location as well as scale and other parameters has been introduced. To check the superiority of the proposed loss function over some existing and exploited loss functions such as squared error loss function (SELF), general entropy loss function (GELF), LINEX loss function and Logarithmic-SELF (LSELF), we have calculated the Bayes estimators of the parameter theta of exponential distribution under SELF, GELF, LINEX loss function, Logarithmic-SELF (LSELF) and the proposed exponential squared error loss function (ESELF) for complete sample from the exponential distribution. A data set has been considered to show its application to the real problems. The simulation study is carried out to compare the performance of Bayes estimators in terms of their posterior risks.

In statistical literature, various lifetime distributions have been proposed for analysing the lifetime data.Lindley distribution is one of them.It is a one-parameter model.But its suitability is restricted to the data having an increasing failure rate.In many real situations, data may possess other shapes of hazard rate function like-decreasing, bathtub, or up-sided down bathtub, etc.In this research article, we propose a generalization of Lindley distribution which is capable to fit a variety of datasets having different shapes of hazard rate function.Several statistical characteristics and properties of this distribution are also studied.Finally, to show the suitability and applicability of the proposed model in real scenarios two different datasets have been considered.

A new point estimation method based on Kullback-Leibler divergence of survival functions (KLS), measuring the distance between an empirical and prescribed survival functions, has been used to estimate the parameter of Lindley distribution. The simulation studies have been carried out to compare the performance of the proposed estimator with the corresponding Least square (LS), Maximum likelihood (ML) and Maximum product spacing (MPS) methods of estimation.

In this paper, a new lifetime distribution is introduced on the basis of SS transformation as suggested by Kumar et al. (2015(a)). The considered baseline distribution is Lindley(θ) −distribution. Some of the statistical properties of this new distribution such as MGF, Mean, Median, Skewness and Kurtosis have been studied. A real dataset has been considered and AIC, BIC, K-S test value with its pvalue are calculated for this new distribution and for some other distribution too in order to show its application and superiority as compared to some other distributions.

Kumar, D.; Department of Statistics, Banaras Hindu UniversityIndia; email: dinesh.ra77@gmail.com

The present paper describes the Bayes estimators of parameters of inverse Weibull distribution for complete, type I and type II censored samples under general entropy and squared error loss functions. The proposed estimators have been compared on the basis of their simulated risks (average loss over sample space). A real-life data set is used to illustrate the results.

In this paper, we propose Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under general Entropy loss function for a censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under squared error loss function and maximum likelihood estimators through their simulated risks (average loss over sample space).