Generalized gamma distribution

About: Generalized gamma distribution is a research topic. Over the lifetime, 1146 publications have been published within this topic receiving 27832 citations.

A Generalization of the Gamma Distribution

Abstract: This paper concerns a generalization of the gamma distribution, the specific form being suggested by Liouville's extension to Dirichlet's integral formula [3]. In this form it also may be regarded as a special case of a function introduced by L. Amoroso [1] and R. d'Addario [2] in analyzing the distribution of economic income. (Also listed in [4] and [5].) In essence, the generalization (1) herein is accomplished by supplying a positive parameter, $p$, as an exponent in the exponential factor of the gamma distribution. The moment generating function is shown, and cumulative probabilities are related directly to the incomplete gamma function (tabulated in [6]). Distributions are given for various functions of independent "generalized gamma variates" thus defined, special attention being given to the sum of such variates. Convolution results occur in alternating series form, with coefficients whose evaluation may be tedious and lengthy. An upper bound is provided for the modulus of each term, and simplified computation methods are developed for some special cases. A corollary is derived showing that the researches of Robbins in [7] apply to a larger class of problems than was treated in [7]. Extensions of his methods lead to iterative formulae for the coefficients in series obtained for an even larger class of problems.

Generalized Exponential Distributions

Abstract: Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

Exponentiated exponential family: an alternative to gamma and weibull distributions

Abstract: Summary In this article we study some properties of a new family of distributions, namely Exponentiated Exponentialdistribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribution. We present two reall ife data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.

On distances in uniformly random networks

Abstract: The distribution of Euclidean distances in Poisson point processes is determined. The main result is the density function of the distance to the n-nearest neighbor of a homogeneous process in Ropfm, which is shown to be governed by a generalized Gamma distribution. The result has many implications for large wireless networks of randomly distributed nodes

User mobility modeling and characterization of mobility patterns

Abstract: A mathematical formulation is developed for systematic tracking of the random movement of a mobile station in a cellular environment. It incorporates mobility parameters under the most generalized conditions, so that the model can be tailored to be applicable in most cellular environments. This mobility model is used to characterize different mobility-related traffic parameters in cellular systems. These include the distribution of the cell residence time of both new and handover calls, channel holding time, and the average number of handovers. It is shown that the cell residence time can be described by the generalized gamma distribution. It is also shown that the negative exponential distribution is a good approximation for describing the channel holding time.