*Correspondence: [email protected] 2Departamento de Estatística, Universidade de Brasília, 70910-900 Brasília, DF, Brazil Full list of author information is available at the end of the article Abstract For any continuous baseline G distribution, Zografos and Balakrishnan (Statistical Methodology 6:344–362, 2009) introduced the gamma-generated family of distributions with an extra shape parameter. ...

In structural engineering, a distinction can be made between a structure’s resistance and its stress. A failure may then be defined as the event in which—due to deterioration—the resistance drops below the stress. This paper proposes a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural syst...

We derive a closed form solution for the Kullback-Leibler divergence between two generalized gamma distributions. These notes are meant as a reference and provide a guided tour towards a result of practical interest that is rarely explicated in the literature. 1 The Generalized Gamma Distribution The origins of the generalized gamma distribution can be traced back to work of Amoroso in 1925 [1,...

The paper is concerned with posterior analysis of exponentiated gamma distribution for type II censored samples. The expressions for Bayes estimators and associated risks have been derived under different priors. The entropy and quadratic loss functions have been assumed for estimation. The posterior predictive distributions have been obtained and corresponding intervals have been constructed. ...

In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated

• 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 l...

Delayed effects for pharmacodynamic responses can be observed for many signal transduction processes. Three approaches are summarized in this report to describe such effects caused by cascading steps: stochastic process model, gamma distribution function, and transit compartment model. The gamma distribution function, a probability density function of the waiting time for the final step in a st...

In this paper, a Bayesian approach is proposed to estimate ood quan-tiles while taking the statistical uncertainties into account. Predictive excee-dence probabilities of annual maximum discharges are obtained using the three-parameter generalised gamma distribution. The parameters of this distribution are assumed to be random quantities rather than deterministic quantities and to have a prior ...