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.
Highlights
Models are at the heart of almost all statistical work
A statistical model is a classification of probability distributions. e distribution family can be parametric, semiparametric, or nonparametric
E generated family of distributions has a large influence on the quality of statistical analysis procedures, and much effort has gone into developing new statistical models
Summary
Models are at the heart of almost all statistical work. A statistical model is a classification of probability distributions. e distribution family can be parametric, semiparametric, or nonparametric. Most modifications of the log-logistic model in the statistical literature have been derived by adding extra parameters to control the shape of the skewness (or asymmetry) and the kurtosis of the distribution; see the exponentiated LL distribution [13], beta LL distribution [14], gamma LL distribution [15], Marshall–Olkin LL distribution [16], transmuted LL distribution [17], cubic transmuted LL distribution [18], McDonald LL distribution [19], and alpha power transformed LL distribution [20, 21]. (i) adding extra parameter(s) to the distribution enhances flexibility, but even so, such practices usually result in reparameterization issues; (ii) the number of model parameters is increased, causing difficulty in estimating the model’s parameters; (iii) some extending techniques reduce the tractability of the cdf, making manual computation of statistical properties more difficult; and (iv) other generalization techniques complicate the pdf, resulting in computational issues; incorporating new extra parameters into existing models increases flexibility, which is a desirable feature.
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