The order-q Tsallis (Hq ) and Rényi entropy (Kq ) receive broad applications in the statistical analysis of complex phenomena. A generic problem arises, however, when these entropies need to be estimated from observed data. The finite size of data sets can lead to serious systematic and statistical errors in numerical estimates. In this paper, we focus upon the problem of estimating generalized...

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate employing projection onto a exponential family. Its theoretical properties are established parallelly those of the when belongs curved families. It is also demonstrated that asymptotically ...

In this paper, we consider the Bayesian analysis of the Marshall-Olkin bivariate Weibull distribution. It is a singular distribution whose marginals are Weibull distributions. This is a generalization of the Marshall-Olkin bivariate exponential distribution. It is well known that the maximum likelihood estimators of the unknown parameters do not always exist. The Bayes estimators are obtained w...

Bayes and classical estimators have been obtained for two-parameter exponentiated-Weibull distribution when sample is available from type-II censoring scheme. Bayes estimators have been developed under squared error loss function as well as under LINEX loss function using non-informative type of priors for the parameters. Besides, the generalized maximum likelihood estimators and the usual maxi...

This paper is the first of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In this paper a Bayesian analysis of this problem is presented, the optimal properties of the Bayes estimators are discussed, and as an example of the formalism, closed form expressions for the Bayes estimators for the moments of the Shannon ent...

The aim of the present paper is to obtain Bayes estimators for the oospring mean of a simple branching process with a power series oospring probability distribution. We study the sensitivity behavior of the obtained estimators with respect to the choice of the loss function. We propose a minimax criterion using the Bayes risk for ranking the eeectiveness (in the sense of robustness) of the loss...

Abstract: This paper is the first of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In this paper a Bayesian analysis of this problem is presented, the optimal properties of the Bayes estimators are discussed, and as an example of the formalism, closed form expressions for the Bayes estimators for the moments of the S...

Abstract In this paper, the estimation of R=Pr(Y < Y), when X and Y are two generalized inverted exponential distributions with different parameters is considered. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. Exact and asymptotic confidence intervals of R are constructed using both exact and asymptotic distributions. Assuming that the common scale pa...