المستخلص: |
Some generalizations of the Rayleigh density function are reviewed. An entropy-based transformation G(x) is proposed, using the distribution function F(x) and the Reliability function R(x) of a continuous random variable X, modeling the time-to-failure of a given component. The derivative, G(X) = g(x), is found to be a “density function” which is a peculiar form of one of the reviewed generalizations. The behavior of its failure rate is investigated, and the mean time-to-failure rate is investigated, and the mean time-to-failure (MTF) is evaluated. The parameter of the derived density g(x) is estimated using two different methods of estimation, namely, the method of moments and the maximum likelihood method. The resulting estimates and are not coinciding.
|