Extended Half-Power Exponential Distribution with Applications to COVID-19 Data

In this paper, the Extended Half-Power Exponential (EHPE) distribution is built on the basis of the Power Exponential model. The properties of the EHPE model are discussed: the cumulative distribution function, the hazard function, moments, and the skewness and kurtosis coefficients. Estimation is carried out by applying maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to assess the performance of ML estimates. To illustrate the usefulness and applicability of EHPE distribution, two real applications to COVID-19 data in Chile are discussed

Discrete generalized half-normal distribution and its applications in quantile regression

A new discrete two-parameter distribution is introduced by discretizing a generalized half-normal distribution. The model is useful for fitting overdispersed as well as underdispersed data. The failure function can be decreasing, bathtub shaped or increasing. A reparameterization of the distribution is introduced for use in a regression model based on the median. The behaviour of the maximum likelihood estimates is studied numerically, showing good performance in finite samples. Three real data set applications reveal that the new model can provide a better explanation than some other competitors

An extension of the slash-elliptical distribution

This paper introduces an extension of the slash-elliptical distribution. This new distribution is generated as the quotient between two independent random variables, one from the elliptical family (numerator) and the other (denominator) a beta distribution. The resulting slash-elliptical distribution potentially has a larger kurtosis coefficient than the ordinary slash-elliptical distribution. We investigate properties of this distribution such as moments and closed expressions for the density function. Moreover, an extension is proposed for the location scale situation. Likelihood equations are derived for this more general version. Results of a real data application reveal that the proposed model performs well, so that it is a viable alternative to replace models with lesser kurtosis flexibility. We also propose a multivariate extension

Likelihood-based inference for the power regression model

In this paper we investigate an extension of the power-normal model, called the alpha-power model and specialize it to linear and nonlinear regression models, with and without correlated errors. Maximum likelihood estimation is considered with explicit derivation of the observed and expected Fisher information matrices. Applications are considered for the Australian athletes data set and also to a data set studied in Xie et al. (2009). The main conclusion is that the proposed model can be a viable alternative in situations were the normal distribution is not the most adequate model

Statistical Inference for a General Family of Modified Exponentiated Distributions

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamma and Weibull. A simulation study and a real application are presented. It is shown that the proposed family of distributions is of interest to applied areas, such as economics, reliability and finances

A note on the Fisher information matrix for the skew-generalized-normal model

In this paper, the exact form of the Fisher information matrix for the skew-generalized normal (SGN) distribution is determined. The existence of singularity problems of this matrix for the skew-normal and normal particular cases is investigated. Special attention is given to the asymptotic properties of the MLEs under the skew-normality hypothesis

A new class of Skew-Normal-Cauchy Distribution

In this paper we study a new class of skew-Cauchy distributions inspired on the family extended two-piece skew normal distribution. The new family of distributions encompasses three well known families of distributions, the normal, the two-piece skew-normal and the skew-normal-Cauchy distributions. Some properties of the new distribution are investigated, inference via maximum likelihood estimation is implemented and results of a real data application, which reveal good performance of the new model, are reporte

A new class of Skew-Normal-Cauchy Distribution

In this paper we study a new class of skew-Cauchy distributions inspired on the family extended two-piece skew normal distribution. The new family of distributions encompasses three well known families of distributions, the normal, the two-piece skew-normal and the skew-normal-Cauchy distributions. Some properties of the new distribution are investigated, inference via maximum likelihood estimation is implemented and results of a real data application, which reveal good performance of the new model, are reporte

Scale Mixture of Rayleigh Distribution

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution