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 sub-models, 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.