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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Shrnutí: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.
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ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2016.1238088