Topp-Leone Odd Fréchet Generated Family of Distributions with Applications to COVID-19 Data Sets

Recent studies have pointed out the potential of the odd Fréchet family(or class)of continuous distributions in fitting data of all kinds.In this article,we propose an extension of this family through the so-called“Topp-Leone strategy”,aiming to improve its overall flexibility by adding a shape parameter.The main objective is to offer original distributions with modifiable properties,from which adaptive and pliant statistical models can be derived.For the new family,these aspects are illustrated by the means of comprehensive mathematical and numerical results.In particular,we emphasize a special distribution with three parameters based on the exponential distribution.The related model is shown to be skillful to the fitting of various lifetime data,more or less heterogeneous.Among all the possible applications,we consider two data sets of current interest,linked to the COVID-19 pandemic.They concern daily cases confirmed and recovered in Pakistan from March 24 to April 28,2020.As a result of our analyzes,the proposed model has the best fitting results in comparison to serious challengers,including the former odd Fréchet model.

Generalized Truncated Fréchet Generated Family Distributions and Their Applications

Understanding a phenomenon from observed data requires contextual and efficient statistical models.Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations.Modern examples include the distributions of the truncated Fréchet generated family.In this paper,we go even further by introducing a more general family,based on a truncated version of the generalized Fréchet distribution.This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters,as well as the skewness and weight of the tails.We also investigate the main functions of the new family,stress-strength parameter,diverse functional series expansions,incomplete moments,various entropy measures,theoretical and practical parameters estimation,bivariate extensions through the use of copulas,and the estimation of the model parameters.By considering a special member of the family having the Weibull distribution as the parent,we fit two data sets of interest,one about waiting times and the other about precipitation.Solid statistical criteria attest that the proposed model is superior over other extended Weibull models,including the one derived to the former truncated Fréchet generated family.

On the Genesis of the Marshall-Olkin Family of Distributions via the T-X Family Approach: Statistical Modeling

In the last couple of years,there Has been an increased interest among the statisticians to dene new families of distributions by adding one or more additional parameter(s)to the baseline distribution.In this regard,a number of families have been introduced and studied.One such example is the Marshall-Olkin family of distributions that is one of the most prominent approaches used to generalize the existing distributions.Whenever,we see a new method,the natural questions come in to mind are(i)what are the genesis of the newly proposed method and(ii)how did the proposed method is obtained.No doubt,the Marshall-Olkin family is a very useful method and has attracted the researchers.But,unfortunately,the authors failed to provide the explanation about the genesis of the method that how this family of distributions is obtained.To address this issue,in this article,an attempt Has been made to provide a straight forward computation about the genesis of the Marshall-Olkin family that somehow completes its derivation.The genesis of the Marshall-Olkin family is based on the T-X family approach.Furthermore,we have showed that other extensions of the Marshall-Olkin family can also be obtained via the T-X family method.Finally,a real-life application form insurance science is presented to illustrate the newly proposed extension of the Marshall-Olkin family.

The Bivariate Transmuted Family of Distributions:Theory and Applications

The bivariate distributions are useful in simultaneous modeling of two random variables.These distributions provide a way to model models.The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed.The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon.Statistical properties of the new family of distributions are explored which include marginal and conditional distributions,conditional moments,product and ratio moments,bivariate reliability and bivariate hazard rate functions.The maximum likelihood estimation(MLE)for parameters of the family is also carried out.The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull(BTW)distribution.The new bivariate transmuted Weibull distribution is explored in detail.Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions,product,ratio and conditional momenst.The hazard rate function of the BTW distribution is obtained.Parameter estimation of the BTW distribution is also done.Finally,real data application of the BTW distribution is given.It is observed that the proposed BTW distribution is a suitable fit for the data used.

An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap,Regression and Applications

This paper introduces a new rich family of distributions based on mixtures and the so-called Marshall-Olkin family of distributions.It includes a wide variety of well-established mixture distributions,ensuring a high ability for data fitting.Some distributional properties are derived for the general family.The Weibull distribution is then considered as the base-line,exhibiting a pliant four-parameter lifetime distribution.Five estimation methods for the related parameters are discussed.Bootstrap confidence intervals are also considered for these parameters.The distribution is reparametrized with location-scale parameters and it is used for a lifetime regression analysis.An extensive simulation is carried out on the esti-mation methods for distribution parameters and regression model parameters.Applications are given to two practical data sets to illustrate the applicability of the new family.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

On Modeling the Medical Care Insurance Data via a New Statistical Model

Proposing new statistical distributions which are more flexible than the existing distributions have become a recent trend in the practice of distribution theory.Actuaries often search for new and appropriate statistical models to address data related to financial and risk management problems.In the present study,an extension of the Lomax distribution is proposed via using the approach of the weighted T-X family of distributions.The mathematical properties along with the characterization of the new model via truncated moments are derived.The model parameters are estimated via a prominent approach called the maximum likelihood estimation method.A brief Monte Carlo simulation study to assess the performance of the model parameters is conducted.An application to medical care insurance data is provided to illustrate the potentials of the newly proposed extension of the Lomax distribution.The comparison of the proposed model is made with the(i)Two-parameter Lomax distribution,(ii)Three-parameter models called the half logistic Lomax and exponentiated Lomax distributions,and(iii)A four-parameter model called the Kumaraswamy Lomax distribution.The statistical analysis indicates that the proposed model performs better than the competitive models in analyzing data in financial and actuarial sciences.

The Odd Log-Logistic Generalized Gompertz Distribution:Properties,Applications and Different Methods of Estimation

We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.