The general properties of the gamma distribution, which has several applications in meteorology, are discussed. A short review of the general properties of good statistical estimators is given. This is applied to the gamma distribution to show that the maximum likelihood estimators are jointly sufficient. A new, simple approximation of the likelihood solutions is given, and the efficiency of th...

1. Prior Sensitivity In all our examples, we placed a Gamma prior on the precision parameter θ with parameters α = 0.001 and β = 0.001. This precision parameter, unknown to us a priori, controls the smoothness of the GP prior. We investigate the sensitivity of our results to the Gamma prior specification using the Egyptian HCV data. In the first plot of Figure 1, we show the prior and posterior...

A common way of allowing heterogeneity between individuals in models for lifetime data is to introduce an unobservable individual random effect Z. In a proportional hazards framework, the individual’s hazard becomes zhb(t) where hb(t) is the baseline hazard. The random variable Z is often assumed to follow the Gamma or Inverse Gaussian distribution. We develop here diagnostic tests for these as...

A method is presented for estimating relative mutation rates or relative effective population sizes, under the hypothesis of adaptively neutral allelic variation. This method was applied to seven surveys of electrophoretic variation. It was observed that electrophoretic mutation rates so obtained follow the gamma distribution and, in Drosophila, are positively correlated with the molecular weig...

A series repairable system not only is one of the classical reliability models but is also the usually used model in practice. In this paper, a method for calculating system availability for series repairable system is studied. From the states of components, this methodology uses a gamma distribution to model the material degradation, and the impact of imperfect maintenance actions on the syste...

The paper studies changes in daily precipitation records at the National Observatory, Athens, during the period 1891–2004. This is the longest available time series of precipitation for Greece. The results show that both the shape and scale parameter of a fitted two parameter gamma distribution for the last two decades do show a significant difference of these parameters, when compared to any p...

It is well known that unobserved heterogeneity can produce misleading estimates in survival analysis (see for example, Allison, 1995, p.233). The goal of this paper is to show how to estimate and apply a single event timing model with heterogeneity to real data with SAS. We consider three different models: An Exponential-gamma model, when individual-level time-to-event is exponentially distribu...

Nowadays, the search for a distribution capable of modeling the probability density function (PDF) of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging still continues. Here, a family of PDFs alternative to the widely accepted Log-Normal and Gamma-Gamma distributions is proposed to model the PDF of the received optical power in free-space optic...

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating func...