Raindrop size distribution (DSD) retrieval from remote radar measurements or from in situ disdrometer measurements is an important area of research. If the shape ( ) and slope ( ) of a three-parameter gamma distribution n(D) N0D exp( D ) are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified to a two-parameter DSD, that is, a constrained gamma ...

We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors parameter. derived The posterior density with mean and variance using which the inverse exponential distribution, chi-square Gamma standard Levy distribution as prior. And we based on general entropy loss function (GELF) Simulation method to obtain...

A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mix...

To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Cl...

In modeling the rate of return associated with financial instruments, common probability distributions include the lognormal, gamma, and Weibull distributions. Furthermore, the method of maximum likelihood is widely used to estimate the unknown parameters of distributions due to the highly desirable properties of maximum likelihood estimators (MLEs). These properties include asymptotic unbiased...

This paper proposes a semi-parametric software reliability model (SRM) based on a mixed gamma distribution, so-called the mixed gamma SRM. In addition, we develop the parameter estimation method for the mixed gamma SRM. Concretely, the estimation method is based on the Bayesian estimation and the parameter estimation algorithm is described by MCMC (Markov chain Monte Carlo) method with grouped ...

We consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called "mean orthogonal class" is closed under convolution. A previous characterization of the compound gamma characterization of random sums is revisited and clarified. A new character...

abstract agricultural scientists have developed considerable interest in modeling and generation of rainfall as new ways of analyzing rainfall data and assessing its impact on agriculture. a combination of markov chain and gamma distribution function is recognized as a simple approach and is demonstrated to be effective in generating daily rainfall data for many environments. thus the availabil...

Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution by Joseph McDonald Malwane Ananda, Examination Committee Chair Professor of Mathematical Sciences University of Nevada, Las Vegas The log-gamma model has been used extensively for flood frequency analysis and is an important distribution in reliability, medical and other areas of lifetime testing. Conventiona...

In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, exponentiated gamma gamma-modified gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed studied. Mathematical properties including moments, mean deviations, Bonferroni Lorenz curves, order st...