Research Article A New Version of Weighted Weibull Distribution: Modelling to COVID-19 Data Amani Abdullah Alahmadi, 1 Mohammed Alqawba, 2 Waleed Almutiry , 2 A. W. Shawki, 3 Sharifah Alrajhi, 4 Sanaa Al-Marzouki, 4 and Mohammed Elgarhy 5 1 College of Science and Humanities, Shaqra University, Shaqra, Saudi Arabia 2 Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass, Saudi Arabia 3 Central Agency for Public Mobilization & Statistics (CAPMAS), Cairo, Egypt 4 Statistics Department, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia 5 e Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt Correspondence should be addressed to Mohammed Elgarhy; m_elgarhy85@sva.edu.eg Received 18 September 2021; Revised 31 October 2021; Accepted 14 March 2022; Published 21 April 2022 Academic Editor: Sovan Samanta Copyright © 2022 Amani Abdullah Alahmadi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this study, we will look at a new flexible model known as the new double-weighted Weibull distribution. e new Weibull double-weighted distribution model is highly versatile because numerous submodels are included. e proposed model is very flexible because its density function has many shapes; it can be right skewness, decreasing, and unimodal. Also, the hazard rate function can be increasing, decreasing, up-side-down, and J-shaped. Diverse features of the novel are computed. ese qualities include moments, incomplete moments, and Lorenz and Bonferroni curves and quantiles, as well as entropy and order statistics. e maximum likelihood approach is used to estimate the model’s parameters. In order to evaluate the accuracy and performance of maximum likelihood estimators, simulation data are presented. e utility and adaptability of the proposed model are demonstrated by utilizing three significant datasets: daily fatalities confirmed cases of COVID-19 in Egypt and Georgia and relief times of twenty patients using an analgesic. 1. Introduction In 1951, Swedish scientist Walled Weibull created the Weibull (Wei) distribution. e Wei distribution is a fre- quently used distribution for modelling lifetime data in dependability where the hazard rate function is monotone. However, when the true hazard shape is unimodal or bathtub, the two-parameter Wei distribution is inadequate in many applications, such as lifetime analysis. To deal with bathtub-shaped failure rates, many generalizations of the Wei distribution have been proposed in the statistical literature. e probability density function (pdf ) and cumulative distribution function (cdf ) have the following shape: g(x) αβx β− 1 e − αx β , x > 0, α, β > 0, (1) G(x) 1 − e − αx β , x > 0, (2) where β is a positive shape parameter and α is a positive scale parameter. Weighted (W) distributions may be used to increase comprehension of standard distributions as well as provide techniques for extending distributions for additional flexi- bility in fitting a dataset. A W distribution can be obtained in a variety of ways. In 1934, Fisher proposed the concept of W distribution. Rao [1] and Patil and Rao [2] discuss appli- cations of a W distribution to biased samples in many disciplines such as medicine, ecology, dependability, and branching processes (1978). Patil and Rao [2] suggested a Hindawi Discrete Dynamics in Nature and Society Volume 2022, Article ID 3994361, 12 pages https://doi.org/10.1155/2022/3994361