A new family of distributions using a trigonometric function: Properties and applications in the healthcare sector.

Probability distributions play a pivotal and significant role in modeling real-life data in every field. For this activity, a series of probability distributions have been introduced and exercised in applied sectors. This paper also contributes a new method for modeling continuous data sets. The proposed family is called the exponent power sine-G family of distributions. Based on the exponent power sine-G method, a new model, namely, the exponent power sine-Weibull model is studied. Several mathematical properties such as quantile function, identifiability property, and rth moment are derived. For the exponent power sine-G method, the maximum likelihood estimators are obtained. Simulation studies are also presented. Finally, the optimality of the exponent power sine-Weibull model is shown by taking two applications from the healthcare sector. Based on seven evaluating criteria, it is demonstrated that the proposed model is the best competing distribution for analyzing healthcare phenomena.

A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data.

The word extreme events refer to unnatural or undesirable events. Due to the general destructive effects on society and scientific problems in various applied fields, the study of extreme events is an important subject for researchers. Many real-life phenomena exhibit clusters of extreme observations that cannot be adequately predicted and modeled by the traditional distributions. Therefore, we need new flexible probability distributions that are useful in modeling extreme-value data in various fields such as the financial sector, telecommunications, hydrology, engineering, and meteorology. In this piece of research work, a new flexible probability distribution is introduced, which is attained by joining together the flexible Weibull distribution with the weighted T-X strategy. The new model is named a new flexible Weibull extension distribution. The distributional properties of the new model are derived. Furthermore, some frequently implemented estimation approaches are considered to obtain the estimators of the new flexible Weibull extension model. Finally, we demonstrate the utility of the new flexible Weibull extension distribution by analyzing an extreme value data set.

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data.

In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.