[0,1] Truncated Generalized Gamma – Generalized Gamma Distribution

Abstract

In this paper, we introduce a new family of continuous distributions based on interval [0,1] truncated generalized gamma distribution. [0,1] truncated generalized gamma-generalized gamma distribution is discussed as a special case. The cumulative distribution function, the rth moment, the mean, the variance, the skewness, the kurtosis, the mode, the median, the characteristic function, the reliability function and the hazard rate function are obtained for the distribution under consideration. It is well known that an item fails when a stress to which it is subjected exceeds the corresponding strength. In this sense, strength can be viewed as "resistance to failure". Good design practice is such that the strength is always greater than the expected stress. The safety factor can be defined in terms of stress and strength as stress/strength. So, the [0,1] truncated generalized gamma-generalized gamma stress-strength model with different parameters will be derived here. The Shannon entropy and relative entropy will be derived also.