On Finite Gamma Mixtures and Their Properties

Abstract

The concept of finite mixture has contributed immensely in search of more flexible distributions that are in a position to capture data heterogeneity. One parameter Lindley distribution as the first case of a finite mixed gamma distribution has been generalized up to five parameters and goodness of fit measures done. Based on the available literature, Lindley and its generalizations has been extensively applied in modeling of lifetime data. Generalized cases of Lindley distribution prove to be more flexible than one parameter Lindley in modeling lifetime data. However, Lindley and its generalizations have not been extensively compared to other finite gamma mixtures. In this project, the goal is to study finite gamma mixtures and their applications to lifetime data. Similarly, finite gamma mixtures have been constructed up to three component and their statistical properties studied. Selected constructed finite gamma mixtureswere fitted to a lifetime data regarding carbon fiber breaking stress recorded by Nichols and Padget (2006). The model parameters were estimated using method of moments (MOM) and maximum likelihood (MLE) techniques. The results of one parameter selected distributions proved that Suja, Rama, Aradhana, Sujatha, Akash and Shanker were better fit than Lindley distribution. Based on the selected distributions two parameter, it was established that QSD, AG2PAD, QAD, AG2PSD were more flexible than AG2PLD while G2PSD performed worse than AG2PLD. Based on the selected three parameter distributions fitted, AG3PLD was a better fit than AG3PAD and AG3PSD.