Abstract:
This study is concerned with finding a statistical distribution that deals with a Neutrosophic random variable and Neutrosophic parameters called Neutrosophic Hybrid Weibull Inverse Weibull (NHWIW) distribution. The basic functions of proposed distribution are found, as well as many statistical properties of distribution with an estimation of the model parameters in three different techniques, with a Monte Carlo simulation to determine the estimation efficiency of NHWIW distribution, with a comparison with three measures to determine the best method for estimation. A practical application is also conducted on two types of Neutrosophic real data, the first represented by mortality data for children under five years of age, and the second is COVID-19 in Netherlands for thirty days, where the analysis efficiency of the NHWIW distribution is determined by comparing it with six other distributions using 4 information criteria and 4 statistical measures, which showed the efficiency and flexibility of NHWIW distribution.
Keywords: HWG-family, Neutrosophic data, Bias, Cramér-von Mises, and flexibility.


