A Bayesian approach for non-homogeneous gamma degradation processes

A Bayesian approach based on the Markov Chain Monte Carlo technique is proposed for the non-homogeneous gamma process with power-law shape function. Vague and informative priors, formalized on some quantities having a “physical” meaning, are provided. Point and interval estimation of process parameters and some functions thereof are developed, as well as prediction on some observable quantities that are useful in defining the maintenance strategy is proposed. Some useful approximations are derived for the conditional and unconditional mean and median of the residual life to reduce computational time. Finally, the proposed approach is applied to a real dataset.     

Bayesian statistical inference of the loglogistic model with interval-censored lifetime data

Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods.     

Computation of the polygamma functions

An algorithm is presented for computing the psi(digamma) and other polygamma functions.     

Bayesian analysis of the linear regression model with an edgeworth series prior distribution

The purpose of the present investigation 1s to observe the effect of departure from normahty of the prior distribution of regresslon parameters on the Bayman analysis of a h e a r regresslon model Assuming an Edgeworth serles prior distribution for the regresslon coefficients and gamma prior for the disturbances precision, the expressions for the posterlor distribution, posterlor mean and Bayes risk under a quadratic loss function are obtalned The results of a numerical evaluation are also analyzed     

Statistical inference for reciprocal gamma diffusion process

We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite number of discrete eigenfunctions (Bessel polynomials) and eigenfunctions related to a continuous part of the spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.     

Bayesian estimation of incomplete data using conditionally specified priors

In this article, a class of conjugate prior for estimating incomplete count data based on a broad class of conjugate prior distributions is presented. The new class of prior distributions arises from a conditional perspective, making use of the conditional specification methodology and can be considered as the generalization of the form of prior distributions that have been used previously in the estimation of incomplete count data well. Finally, some examples of simulated and real data are given.     

On A method for selecting a distributional model

A method for selecting a distributional model for a random variable, given a random sample of observations of it, is studied for various cases. The problems considered include those of choosing between the Weibull and lognormal distributions, between the lognormal and gamma distributions, and between the gamma and Weibull distributions, as well as choosing one of the three. Simulation studies were performed to estimate probabilities of correct selection for the method when it is applied to these problems     

A Reparameterisation Of A Bivariate Gamma Extension

Becker and Roux (1981) invebiiyated a bivariate gamma extension based on a piausible physica! model. This paper introduces a useful reparameterisation of this bivariate gamma extension. Based on he suggested reparameterisation, a procedure that may be utilised to test for bivariate independence is discussed for a special case of the gamma extension     

Bhattacharyya and Kshirsagar Bounds in Generalized Gamma Distribution

In this article, we consider the exact computation of the famous halfspace depth (HD) and regression depth (RD) from the view of cutting a convex cone with hyperplanes. Two new algorithms are proposed for computing these two notions of depth. The first one is relatively straightforward but quite inefficient, whereas the second one is much faster. It is noteworthy that both of them can be implemented to spaces with dimension beyond three. Some numerical examples are also provided in what follows to illustrate the performances.