[0,1] Truncated Fréchet-Weibull and Fréchet Distributions

Document Type: Research Paper

Authors

Department of mathematics, Education College, University of Mustansiriyah, Baghdad, Iraq.

Abstract

In this paper, we introduce a new family of continuous distributions based on [0, 1] Truncated Fréchet distribution. [0, 1] Truncated Fréchet Weibull ([0, 1] ) and [0, 1] Truncated Fréchet ([0, 1] ) 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]  strength-stress and the [0, 1]  strength-stress models with different parameters will be derived here. The Shannon entropy and Relative entropy will be derived also.

Keywords

Main Subjects

References

[1]      Abid, S. H., & Hassan, H. A. (2015). The Beta Marshall-Olkin Extended Uniform Distribution. Journal of safety engineering, 4(1), 1-7.
[2]      Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in statistics-theory and methods, 31(4), 497-512.
[3]      Gradshteyn, I. S., & Ryzhik, I. M. (2014). Table of integrals, series, and products. Academic press.
[4]      Gupta, A. K., & Nadarajah, S. (2005). On the moments of the beta normal distribution. Communications in statistics-theory and methods, 33(1), 1-13.
[5]      Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43.
[6]      Jamjoom, A. A., & Al-Saiary, Z. A. (2012). Computing the moments of order Statistics from independent nonidentically distributed exponentiated Frechet variables. Journal of probability and statistics, 2012.
[7]      Maria do Carmo, S. L., Cordeiro, G. M., & Ortega, E. M. (2015). A new extension of the normal distribution. Journal of data science, 13(2), 385-408.
International Journal of Research in Industrial Engineering

Volume 7, Issue 1
Spring 2018
Pages 106-135

Files

Share

How to cite

Statistics