Properties with application to medical data for new inverse Rayleigh distribution utilizing neutrosophic logic
Alaa M. Abd El-latif, Fatimah A. Almulhim, Nooruldeen A. Noori, Mundher A. Khaleel, Basim S. O. Alsaedi
Abstract
This study proposes a continuous probability distribution called the hybrid Weibull inverse Rayleigh distribution (HWIR) with three parameters. This distribution is then expanded to deal with neutrosophic data, where neutrosophic random variables and parameters are considered based on the direct neutrosophic method. Our methodology consists of integrating the inverse Rayleigh distribution with the hybrid Weibull family HWG to create the hybrid inverse Rayleigh distribution HWIR and incorporating it into neutrosophic logic. By relying on the extended (direct) neutrosophic distribution method, the neutrosophic distribution, abbreviated as NeHWIR, is generated. Each parameter of the HWIR distribution was modified to include the elements of certainty T, uncertainty I, and failure F, to obtain a more flexible distribution in modeling the original data, and then this distribution is divided into neutrosophic vectors and a data set is created using the simulation method. The study presents some statistical and mathematical properties of the new distribution according to neutrosophic logic, in addition to estimating the parameters using the maximum likelihood method. In addition to conducting a Monte Carlo simulation using eight statistical methods and numerical optimization to determine the bias in the estimated parameters. Finally, regarding the practical aspect, the NeHWIR distribution was applied to two types of real data: the first was the 30-day COVID-19 data for The Netherlands, which was recorded from March 31 to April 30, 2020, and the second type of data was represented by interval estimates of rates. Mortality of infants under five years of age and compared the results with six other distributions using some precision criteria.