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

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

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The shifted exponential-G family of distributions : Properties and applications

Journal of Statistics and Management Systems ◽

10.1080/09720510.2021.1874130 ◽

2021 ◽

pp. 1-33

Author(s):

Joseph Thomas Eghwerido ◽

Friday Ikechukwu Agu ◽

Olayemi Joshua Ibidoja

Keyword(s):

Family Of Distributions

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The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽

10.3390/sym13071114 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1114

Author(s):

Guillermo Martínez-Flórez ◽

Roger Tovar-Falón ◽

María Martínez-Guerra

Keyword(s):

Power Distribution ◽

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Alpha Power ◽

Score Functions ◽

New Family ◽

Two Parameters ◽

Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

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A probabilistic epidemiological model

Model Assisted Statistics and Applications ◽

10.3233/mas-210511 ◽

2021 ◽

Vol 16 (1) ◽

pp. 15-23

Author(s):

Hal M. Switkay

Keyword(s):

United States ◽

United Kingdom ◽

United States Of America ◽

Compartmental Model ◽

The United States ◽

Epidemiological Model ◽

Probabilistic Methods ◽

Infinite Intervals ◽

Best Fit ◽

Family Of Distributions

We construct a model for the progress of the 2020 coronavirus epidemic in the United States of America, using probabilistic methods rather than the traditional compartmental model. We employ the generalized beta family of distributions, including those supported on bounded intervals and those supported on semi-infinite intervals. We compare the best-fit distributions for daily new cases and daily new deaths in America to the corresponding distributions for United Kingdom, Spain, and Italy. We explore how such a model might be justified theoretically in comparison to the apparently more natural compartmental model. We compare forecasts based on these models to observations, and find the forecasts useful in predicting total pandemic deaths.

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A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

Symmetry ◽

10.3390/sym13071226 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1226

Author(s):

Inmaculada Barranco-Chamorro ◽

Yuri A. Iriarte ◽

Yolanda M. Gómez ◽

Juan M. Astorga ◽

Héctor W. Gómez

Keyword(s):

Heavy Tails ◽

Real Data ◽

Rate Function ◽

Data Sets ◽

Estimation Of Parameters ◽

Stochastic Representation ◽

Likelihood Methods ◽

Chi Square ◽

Maximum Likelihood Methods ◽

Family Of Distributions

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.

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On estimation of the PDF and the CDF of the one-parameter polynomial exponential family of distributions

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1910302 ◽

2021 ◽

pp. 1-16

Author(s):

Indrani Mukherjee ◽

Sudhansu S. Maiti ◽

Vijay Vir Singh

Keyword(s):

Exponential Family ◽

Exponential Family Of Distributions ◽

The One ◽

Family Of Distributions

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An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family

Journal of Risk and Financial Management ◽

10.3390/jrfm12040171 ◽

2019 ◽

Vol 12 (4) ◽

pp. 171

Author(s):

Ashis SenGupta ◽

Moumita Roy

Keyword(s):

Entire Range ◽

Goodness Of Fit ◽

Stable Distribution ◽

Real Life ◽

Circular Statistics ◽

Directional Statistics ◽

Symmetric Stable Distribution ◽

Stable Family ◽

Family Of Distributions ◽

Better Than

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

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