The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.

Alpha Power-Kumaraswamy Distribution with An Application on Survival Times of Cancer Patients

The aim of the study is to obtain the alpha power Kumaraswamy(APK)distribution.Some main statistical properties of the APK distribution are investigated including survival,hazard rate and quantile functions,skewness,kurtosis,order statistics.The hazard rate function of the proposed distribution could be useful to model data sets with bathtub hazard rates.We provide a real data application and show that the APK distribution is better than the other compared distributions from the right-skewed data sets.

On a New Version of Weibull Model:Statistical Properties,Parameter Estimation and Applications

In this paper,we introduce a new four-parameter version of the traditional Weibull distribution.It is able to provide seven shapes of hazard rate,including constant,decreasing,increasing,unimodal,bathtub,unimodal then bathtub,and bathtub then unimodal shapes.Some basic characteristics of the proposedmodel are studied,including moments,entropies,mean deviations and order statistics,and its parameters are estimated using the maximum likelihood approach.Based on the asymptotic properties of the estimators,the approximate confidence intervals are also taken into consideration in addition to the point estimators.We examine the effectiveness of the maximum likelihood estimators of the model’s parameters through simulation research.Based on the simulation findings,it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates.Three actual data sets for COVID-19,engineering and blood cancer are used to empirically demonstrate the new distribution’s usefulness inmodeling real-world data.The analysis demonstrates the proposed distribution’s ability in modeling many forms of data as opposed to some of its well-known sub-models,such as alpha powerWeibull distribution.

A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.