Abstract
Development of new flexible distributions for modeling non-negative measurements occuring in lifetime or reliability studies is a prominent research area in Statistics. As being the most favoured positive definite form, the Gamma distribution poses a basis for such improvements. It is well known that transforming a Gamma variable with another continuous random variable (X) creates Gamma-X family of distributions. Following this principle, we here attempted to define the X variable as Folded-Normal distributed which is also positive definite so as to propose a new family of distributions. Named as Gamma Folded-Normal distribution (GFN), our proposal is a generalization of Gamma Half-Normal distribution and contains more freely estimated parameters. This study evaluates some mathematical properties of GFN distribution such as moments and illustrates the estimation procedure for unknown parameters through a simulation study. A separate simulation is also conducted to compare the performance of this new distribution with the Folded-Normal, Half-Normal and Gamma Half-Normal distributions. Besides, the practical importance of our new proposal is illustrated by analyzing a real world data set.
Published Version
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