The generalized odd log-logistic family of distributions: properties, regression models and applications

We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed a...

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Vydáno v:	Journal of statistical computation and simulation Ročník 87; číslo 5; s. 908 - 932
Hlavní autoři:	Cordeiro, Gauss Moutinho, Alizadeh, Morad, Ozel, Gamze, Hosseini, Bistoon, Ortega, Edwin Moises Marcos, Altun, Emrah
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Abingdon Taylor & Francis 24.03.2017 Taylor & Francis Ltd
Témata:	Computer simulation Density Entropy Generated family Logistics Mathematical analysis Mathematical models maximum likelihood moment odd log-logistic order statistic Parameters quantile function Quantiles Regression Regression analysis Rényi entropy
ISSN:	0094-9655, 1563-5163
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Abstract	We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.
AbstractList	We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.
Author	Alizadeh, Morad Altun, Emrah Hosseini, Bistoon Ortega, Edwin Moises Marcos Ozel, Gamze Cordeiro, Gauss Moutinho
Author_xml	– sequence: 1 givenname: Gauss Moutinho surname: Cordeiro fullname: Cordeiro, Gauss Moutinho organization: Departamento de Estatística, Universidade Federal de Pernambuco – sequence: 2 givenname: Morad surname: Alizadeh fullname: Alizadeh, Morad organization: Department of Statistics, Persian Gulf University – sequence: 3 givenname: Gamze surname: Ozel fullname: Ozel, Gamze email: gamzeozl@hacettepe.edu.tr organization: Department of Statistics, Hacettepe University – sequence: 4 givenname: Bistoon surname: Hosseini fullname: Hosseini, Bistoon organization: Department of Statistics, Persian Gulf University – sequence: 5 givenname: Edwin Moises Marcos surname: Ortega fullname: Ortega, Edwin Moises Marcos organization: Departamento de Ciências Exatas, ESALQ-USP, Universidade de São Paulo – sequence: 6 givenname: Emrah surname: Altun fullname: Altun, Emrah organization: Department of Statistics, Hacettepe University
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SubjectTerms	Computer simulation Density Entropy Generated family Logistics Mathematical analysis Mathematical models maximum likelihood moment odd log-logistic order statistic Parameters quantile function Quantiles Regression Regression analysis Rényi entropy
Title	The generalized odd log-logistic family of distributions: properties, regression models and applications
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