Estimation of the maximum divergence of the parameters of the fuzzy triangular distribution based on the quantile function for the year 2022-2023

Abstract

The aim of the research is to generalize the One Parameter Inverse Lindley Distribution for the purpose of expanding the basic distribution properties to suit monotonically descending data using the quantile function principle based on the T-R{Y} distribution class proposed by (Alzaatreh et al., 2014) to generalize the distributions for the purpose of finding the T-IR{Y} distribution class as well as finding a new distribution from this class considering that the distribution of the first variable T follows the inverse exponential distribution with one parameter (Inverse Exponential Distribution) and the variable R has an inverse Lindley distribution with one parameter and the variable Y has an exponential distribution with one parameter, so the resulting expanded distribution is Inverse Exponential- Inverse Lindley- Exponential under the theory of fuzzy sets by converting the resulting distribution to fuzzy based on a formula proposed by (Ali and Nima, 2022) as the resulting distribution is a fuzzy triangular distribution based on the quantile function which is abbreviated as (FIEILE). Estimating the distribution parameters using the Maximum Product Spaceing method using Monte-Carlo simulation experiments, as well as applying it to real data to demonstrate the feasibility of the new distribution.