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

A new flexible family of continuous distributions: the additive Odd-G family

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models

On q-Generalized Extreme Values under Power Normalization with Properties, Estimation Methods and Applications to Covid-19 Data

This paper introduces the q-analogues of the generalized extreme value distribution and its discrete counterpart under power normalization. The inclusion of the parameter q enhances modeling flexibility. The continuous extended model can produce various types of hazard rate functions, with supports that can be finite, infinite, or bounded above or below. Additionally, these new models can effectively handle skewed data, particularly those with highly extreme observations. Statistical properties of the proposed continuous distribution are presented, and the model parameters are estimated using various approaches. A simulation study evaluates the performance of the estimators across different sample sizes. Finally, three distinct real datasets are analyzed to demonstrate the versatility of the proposed 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 Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data

This paper introduces a new flexible probability tool for modeling extreme and zero-inflated count data under different shapes of hazard rates. Many relevant mathematical and statistical properties are derived and analyzed. The new tool can be used to discuss several kinds of data, such as “asymmetric and left skewed”, “asymmetric and right skewed”, “symmetric”, “symmetric and bimodal”, “uniformed”, and “right skewed with a heavy tail”, among other useful shapes. The failure rate of the new class can vary and can take the forms of “increasing-constant”, “constant”, “monotonically dropping”, “bathtub”, “monotonically increasing”, or “J-shaped”. Eight classical estimation techniques—including Cramér–von Mises, ordinary least squares, L-moments, maximum likelihood, Kolmogorov, bootstrapping, and weighted least squares—are considered, described, and applied. Additionally, Bayesian estimation under the squared error loss function is also derived and discussed. Comprehensive comparison between approaches is performed for both simulated and real-life data. Finally, four real datasets are analyzed to prove the flexibility, applicability, and notability of the new class

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

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