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 generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators’ performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution’s flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb’s sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

An extension of the cosine generalized family is presented in this paper by using the cosine trigonometric function and method of parameter induction concurrently. Prominent characteristics of the proposed family along with useful results are extracted. Moreover, two new subfamilies and several special models are also deduced. A four-parameter model called an Extended Cosine Weibull (ECW) with its mathematical properties is studied deeply. Graphical study reveals that the new model adopts right- and left-skewed, symmetrical, and reversed-J density shapes, while all possible monotone and nonmonotone shapes are exhibited by the hazard rate function. The maximum likelihood technique is exercised for parametric estimation, while estimation performance is accessed via Monte Carlo simulation study graphically and numerically. The superiority of the presented model over several outstanding and competing models is confirmed via three reliability and survival dataset applications.

In this paper, we present a review on the log-logistic distribution and some of its recent generalizations. We cite more than twenty distributions obtained by different generating families of univariate continuous distributions or compounding methods on the log-logistic distribution. We reviewed some log-logistic mathematical properties, including the eight different functions used to define lifetime distributions. These results were used to obtain the properties of some log-logistic generalizations from linear representations. A real-life data application is presented to compare some of the surveyed distributions.

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.