A New Version of Weighted Weibull Distribution: Modelling to COVID‐19 Data

Abstract

In this study, we will look at a new flexible model known as the new double-weighted Weibull distribution. The new Weibull double-weighted distribution model is highly versatile because numerous submodels are included. The 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. These qualities include moments, incomplete moments, and Lorenz and Bonferroni curves and quantiles, as well as entropy and order statistics. The 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. The 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.

Bivariate Step-Stress Accelerated Life Tests for the Kavya–Manoharan Exponentiated Weibull Model under Progressive Censoring with Applications

“…We sketched the log-likelihood for every pair of parameters, while fixing the other parameters, as shown in Figures 8, 13 and 18. We plot cdf and pdf of alternative models in Figures 6,7,11,12,16, and 17 for the three real data sets.. We find that the root of the parameter pair is a single point, which assures that the roots are unique. Figure 4, 9 and 14 show TTT plots and the estimated hazard for the three real data sets.…”

“…Furthermore, the analysis of the variability of the skewness and kurtosis on the shape parameters α, β and θ can be investigated based on quantile measures. The median can be obtained by putting p = 0.5 in (11) as…”

“…Mudholkar et al [2] were the first to extend the Weibull distribution with a bathtub-shaped hazard rate, and this extended Weibull has been successfully applied by Xie et al [3]. Other extensions and modified forms of the Weibull with greater flexibility have been proposed; for example, the additive Weibull distribution with a bathtub-shaped hrf by Xie and Lai [4], the EW distribution by Nadarajah et al [5], the transmuted additive Weibull by Elbatal et al [6], the Kumaraswamy transmuted exponentiated modified Weibull by Al-Babtain et al [7], the Burr X EW model by Khalil et al [8], the Marshall-Olkin powergeneralized Weibull distribution by Afify et al [9], truncated Cauchy power Weibull-G by Alotaibi et al [10], a new version of Weighted Weibull distribution by Alahmadi et al [11], exponentiated power generalized Weibull power series family by Aldahlan et al [12], exponentiated truncated inverse Weibull-G by Almarashi et al [13], odd inverse power generalized Weibull by Al-Moisheer et al [14], extended inverse Weibull distribution by Alkarni et al [15], four-parameter Weibull distribution by Abouelmagd et al [16], exponentiated Weibull Weibull distribution by Hassan and Elgarhy [17] among others.…”

Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data

“…The data set given as follows: 11, 11, 8, 11, 12, 15, 21, 20, 18, 15, 14, 21, 16, 11, 28, 29, 19, 14, 19, 29, 34, 34, 46, 46, 47, 36.00, 38, 40, 32, 39, 34, 35, 36, 35, 45, 62. The most recent data, used by [4], revealed the daily fatality confirmed cases attributable to COVID-19. The data consists of 89 observed values, with 18.72 reported deaths on average every day.…”

“…Particularly appropriate to data sets for researching reliability experiments, medical, clinical trials, finance, infant mortality rate, and engineering applications, among other things. The Weibull distribution is a well-liked distribution that may be used to predict how long a product will last, such as a ball bearing, a car part, or electrical insulation see [1][2][3][4][5][6][7][8][9][10]. It is also frequently employed in biological and medical applications.…”