A New Family of Generalized Gamma Distribution and Its Application

Abstract

The mixture distribution is defined as one of the most important ways to obtain new probability distributions in applied probability and several research areas. According to the previous reason, we have been looking for more flexible alternative to the lifetime data. Therefore, we introduced a new mixed distribution, namely the Mixture Generalized Gamma (MGG) distribution, which is obtained by mixing between generalized gamma distribution and length biased generalized gamma distribution is introduced. The MGG distribution is capable of modeling bathtub-shaped hazard rate, which contains special submodels, namely, the exponential, length biased exponential, generalized gamma, length biased gamma and length biased generalized gamma distributions. We present some useful properties of the MGG distribution such as mean, variance, skewness, kurtosis and hazard rate. Parameter estimations are also implemented using maximum likelihood method. The application of the MGG distribution is illustrated by real data set. The results demonstrate that MGG distribution can provide the fitted values more consistent and flexible framework than a number of distribution include important lifetime data; the generalized gamma, length biased generalized gamma and the three parameters Weibull distributions.

The Flexibility of the Generalized Gamma Distribution in Modeling the Fading Based on Kullback-Leibler and Kolmogorov-Smirnov Criteria

“…The GG distribution is employed to model data with dissimilar hazard rates. The probability density function of GG distribution is as [25]:…”

“…in which α 1 and α 2 represent the shape parameters and β is the scale parameter [25], [26]. Another formulation for the GG distribution is as [10]:…”

A New Extended-Gamma Family of Distributions: Properties and Applications

“…One of the important families of distributions in lifetime tests is the extended gamma distribution. The extended generalized gamma distribution is a highly known distribution due to its utility in modelling lifetime data where the hazard rate function is monotone in special cases [4,5].…”

“…Kobayashi considered plane wave diffraction by strip, using the Weiner-Hopf technique [11]. Bachioua [6] generalized Kobayashi gamma function by introducing for the first time a parameter m and representing the new gamma function by [5]:…”

Quantile-Based Estimation of the Finite Cauchy Mixture Model

“…Contributions for specific distributions include, without claiming completeness, the work by Zhang et al [11] who studied a finite mixture Weibull distribution with two components to describe tree diameters for forest data, and Zaman et al [12] who studied chi-squared mixtures of the gamma distribution. Suksaengrakcharoen and Bodhisuwan [13] proposed a mixture of generalized gamma and length biased generalized gamma distributions. Karim et al [14] studied mixtures of Rayleigh distributions by assuming that the weight functions follow chi-square, t and F sampling distributions.…”