Open Access[0, 1] truncated fréchet-gamma and inverted gam-ma distributions
Author(s) -
Salah H. Abid,
Russul K. Abdulrazak
Publication year - 2017
Publication title -
international journal of scientific world
Language(s) - English
Resource type - Journals
ISSN - 2307-9037
DOI - 10.14419/ijsw.v5i2.8363
Subject(s) - kurtosis , mathematics , skewness , gamma distribution , statistics , principle of maximum entropy , probability density function , stress (linguistics) , statistical physics , mathematical analysis , physics , philosophy , linguistics
In this paper, we introduce a new family of continuous distributions based on [0, 1]] truncated Fréchet distribution. [0, 1]] Truncated Fréchet Gamma ([0, 1]] TFG) and truncated Fréchet inverted Gamma ([0, 1]] TFIG) distributions are discussed as special cases. 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 distributions 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 strength and stress as strength/stress. So, the [0, 1]] TFG strength-stress and the [0, 1]] TFIG strength-stress models with different parameters will be derived here. The Shannon entropy and Relative entropy will be derived also.