Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data

Shams Najy Elaiwey^1,*, Mahdi Wahab Neama¹

¹Department of statistics, Faculty of Administration & Economics,  University of Kerbala, Kerbala, Iraq

Emails: shams.n@s.uokerbala.edu.iq; mehdi.wahab@uokerbala.edu.iq

Abstract

In this paper, we propose a novel generalization for one parameter inverse Lindley distribution to fitting monotonically descending data named the T-ILD{Y} distribution class ,   T is one parameter inverse exponential distribution ,  R has an one parameter inverse Lindley distribution , and the variable Y is one parameter exponential distribution, the resulting distribution is inverse exponential- inverse Lindley- exponential (IEILDE). The theory of fuzzy sets  are used by converting the distribution to fuzzy by using  a fuzzy triangular distribution based on the quantile function (FIEILE), the maximum likelihood , and the maximum likelihood, and  the maximum product spacing method were used estimate the parameters of the distribution. We conclude that at cutoff α=0.1, ML is better than the MPS, and at cutoff coefficients α=0.3, 0.5, 0.7, MPS was better than the ML, The higher the cutoff, the better the maximum likelihood method.

Keywords: fuzzy distribution; Quantile Function; monotonically; Lindley distribution Maximum Likelihood; Maximum Product spacing