Modeling COVID-19 Data with a Novel Extended Exponentiated Class of Distributions

Muhammad Arif,Muhammad Aamir,Umair Khalil,Dost Muhammad Khan,Rashad A R Bantan,Mohammed Elgarhy,Gul Rahmat

doi:10.1155/2022/1908161

Abstract

The COVID-19 epidemic has affected every aspect of daily life since December 2019 and caused massive damage to the world. The coronavirus epidemic has affected more than 150 countries around the world. Many researchers have tried to develop a statistical model which can be utilized to analyze the behavior of the COVID-19 data. This article contributes to the field of probability theory by introducing a novel family of distributions, named the novel extended exponentiated class of distributions. Explicit expressions for numerous mathematical characterizations of the proposed family have been obtained with special concentration on a three-parameter submodel of the new class of distributions, named the new extended exponentiated Weibull distribution. The unknown model parameter estimates are obtained via the maximum likelihood estimation method. To assess the performance of these estimates, a comprehensive simulation study is conducted. Three different sets of COVID-19 data are used to check the applicability of the submodel case. The submodel of the new family is compared with three well-known probability distributions. Using different analytical measures, the results demonstrate that the new extended exponentiated Weibull distribution gives promising results in terms of its flexibility and offers data modeling with increasing decreasing, unimodal, and modified unimodal shapes.

Highlights

Probability distributions play a vital role in predicting and defining real-world phenomena
Whereas the cumulative distribution function (CDF) of beta and gamma distributions does not exist in closed form, which creates problems in estimating parameters
A comprehensive simulation study was performed to evaluate the efficiency of the maximum likelihood estimates. e precision of the maximum likelihood estimates is studied through bias, absolute bias, and the mean square error (MSE) for taking different samples by considering different parameter values. e features of the simulation study are as follows: (i) We performed 1000 repetitions from novel extended exponentiated (NEE)-W distribution to quantify the bias and MSE, by taking samples of sizes n 25, 50, . . ., 1000

Summary

Introduction

Probability distributions play a vital role in predicting and defining real-world phenomena. A new contribution has been made to the probability theory by analyzing a new generalized class of distributions called, the Kumaraswamy G (Ku-G) family (see [25] for more details). Researchers have introduced novel families of probability distributions and analyzed COVID19 data through the suggested models. Some authors contributed to the probability theory by introducing new models (see [28, 29]) These distributions have been shown to have less flexibility and a lack of fit in different situations for different real datasets. A special submodal case of the NEE class exhibits that the newly proposed family can model the data having unimodal, decreasing, modified unimodal, and increasing shapes of hazard rates. 4. Mathematical Properties is section article provides the basic mathematical characterizations including, raw moments, quantile function, and moment generating function of the NEE class of distributions. Is the solution of log(eθt + 1) + 2 log t − log(eθ + 1), U has the uniform distribution

Estimation of Parameters and Monte Carlo Simulation Study

Data 1

Data 3

Limitations of the Proposed Model

Future Research Direction