A New Beta Power Generator for Continuous Random Variable: Features and Inference to Model Asymmetric Data

Statistical methodologies have broad applications in sports and other exercise sciences. These methods can be used to predict the winning probability of a team or individual in a match. Due to the applicability of the statistical methods in sports, this paper introduces a new method of obtaining statistical distributions. The new method is called a novel beta power-L family of distributions. Some mathematical characteristics of the new family are obtained. Based on the novel beta power-L family, a special model, namely, a novel beta power Weibull model is studied. Finally, the applicability/usefulness of the novel beta power Weibull distribution is shown by analyzing the time-to-even data taken from different football matches during 1964-2018. The data consist of seventy-eight observations and is representing the waiting time duration of the fastest goal scored ever in the history of football. The fitting results of the novel beta power Weibull distribution are compared with other models. Based on three model selection criteria, it is observed that the proposed novel beta power Weibull model provides a close fit to the waiting time data

Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling

The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric “right skewed” data with long “heavy” tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model

Modelling Coronavirus and Larvae Pyrausta Data: A Discrete Binomial Exponential II Distribution with Properties, Classical and Bayesian Estimation

In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are derived. The shape of the failure rate function is increasing. Moreover, the proposed model is appropriate for modelling equi-, over- and under-dispersed data. The parameter estimation through the classical point of view has been done using the method of maximum likelihood, whereas, in the Bayesian framework, assuming independent beta priors of model parameters, the Metropolis–Hastings algorithm within Gibbs sampler is used to obtain sample-based Bayes estimates of the unknown parameters of the proposed model. A detailed simulation study is carried out to examine the outcomes of maximum likelihood and Bayesian estimators. Finally, two distinctive real data sets are analyzed using the proposed model. These applications showed the flexibility of the new distribution

A Flexible Extension to an Extreme Distribution

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution

A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1)

We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model

Extended Gompertz Distribution: Properties and Estimation under Complete and Censored Data

In this paper, a new flexible model with three-parameter alternative to exponential and Gompertz distributions is proposed. Some of its statistical properties are derived including quantities, moments, incomplete moments, moment of residual and reversed residual life. The parameters are estimated using the maximum likelihood method based on complete and Type II right censored data. We assess the performance of estimators in terms of bias and mean square error using simulation study. Finally, three real data sets are analyzed to illustrate the flexibility of the proposed model