Modelling the COVID‐19 Mortality Rate with a New Versatile Modification of the Log‐Logistic Distribution

Abstract

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

The distribution of COVID-19 mortality

“…The log-logistic distribution has been used to model mortality data ( Muse et al, 2021 ), so we also consider it: where is a location parameter and σ > 0 is a shape parameter. Like the log-normal distribution, we also use 2- and 3-mixtures of log-logistic distributions ( Puente-Ajovín et al, 2020a ): where 0 ≤ p 1 , 1 − p 1 ≤ 1, and where 0 ≤ p 1 , p 2 , 1 − p 1 − p 2 ≤ 1.…”

The Extended Exponential Weibull Distribution: Properties, Inference, and Applications to Real‐Life Data

“…e ExEW distribution is compared to submodels such as the W, EE [41], and EW distributions [16], and other common lifetime distributions including the log-logistic (LL), beta Weibull (BW) [14], beta extended Weibull (BEW) [43], modified beta Weibull (MBW) [44], and tan-loglogistic (TanLL) distributions [45]. e competing models' pdfs are as follows:…”

Bayesian and Non-Bayesian Estimation Methods for Simulating the Parameter of the Akshaya Distribution

“…The generalised Lindley distribution was first introduced in 2011 by Nadarajah et al, who showed that it outperforms gamma, log-normal, Weibull, and exponential distributions when taking bathtub hazard rate into account [12]. In 2021, Mahmood et al [19] published an enlarged Cosine generalised family of distributions for dependability modelling: characteristics and applications with simulation analysis, and Muse et al [20] suggested a new flexible form of the loglogistic distribution. Citations [5], [17], and [6] in 2022 explored a family of produced distributions with applications.…”