The Weibull-G Family of Probability Distributions

By Marcelo Bourguignon, Rodrigo B. Silva, Gauss Moutinho Cordeiro. Journal of Data Science, 2014

621 citations recorded by the source corpus.

The Weibull distribution is the most important distribution for problems in reliability. We study some mathematical properties of the new wider Weibull-G family of distributions. Some special models in the new family are discussed. The properties derived hold to any distribution in this family. We obtain general explicit expressions for the quantile function, ordinary and incomplete moments, generating function and order statistics. We discuss the estimation of the model parameters by maximum likelihood and illustrate the potentiality of the extended family with two applications to real data.

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/46007096b8c46d2d6436d8c28fc46b2cbfb7f49f

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Citations in the corpus

A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension (2020, background): “[12]; Torabi and Montazeri [25]; Tahir et al.”
Generalized Transmuted Family of Distributions: Properties and Applications (2017, background): “[12], Exponentiated half logistic generated family by Cordeiro et al.”
The Kumaraswamy Marshal-Olkin family of distributions (2015, neutral): “[14], exponentiated half-logistic by Cordeiro et al.”
A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications (2014, background): “…by Cordeiro and de Castro (2011), the McDonald-G (Mc-G) by Alexander et al. (2012), the gamma-G by Zografos and Balakrishanan (2012), the transformer (T-X) by Alzaatreh et al. (2013), the Weibull-G by Bourguignon et al. (2014) and the exponentiated half-logistic family by Cordeiro et al. (2014).”
The four-parameter Burr XII distribution: Properties, regression model, and applications (2018, methodology): “…baseline model with parameter vector ξ and consider the Weibull cdf (x) = 1 − exp(−axb) (for x > 0) with positive parameters a and b. Based on this density, Bourguignon et al. (2014) replaced the argument x by G(x; ξ )/G(x; ξ ), where G(x; ξ ) is the reliability function, and defined the cdf of…”
The Weibull-Exponential Distribution: Its Properties and Applications (2015, methodology): “6 has been used to define the pdf and cdf of Weibull-Uniform distribution, Weibull-Weibull distribution, Weibull-Burr XII distribution and Weibull-Normal distribution by Bourguignon et al. (2014).”
A New Weibull Class of Distributions: Theory, Characterizations and Applications (2018, background): “Bourguignon et al. (2014), introduced a distribution given by F (x) = 1− exp { −α [ G (x) G (x) ]β} , x ∈ R.”
WEIBULL-LOMAX DISTRIBUTION: PROPERTIES AND APPLICATIONS (2014, neutral): “[20] proposed the Weibull-G class in uenced by the Zografos-Balakrishnan-G class.”
The Generalized Odd Weibull Generated Family of Distributions:Statistical Properties and Applications (2018, methodology): “We compare the GOWG-N model with Gompertz-normal (Gom-N) model (Alizadeh, et al., 2017a), odd exponentiated half logistic normal (OEHL-N) model (Afify, et al., 2017e), odd Lindley normal (OL-N) model (da-Silva et al., 2017), odd log logistic normal (Braga et al., 2016) model and odd Weibull normal (”
KUMARASWAMY WEIBULL-GENERATED FAMILY OF DISTRIBUTIONS WITH APPLICATIONS (2016, methodology): “In this paper, we introduce and study a new family of continuous distributions called Kumaraswamy Weibull-generated ( ) G KwW family of distributions which is an extension of the Weibull-G family of distributions proposed by Bourguignon in [3].”
The type II Topp-Leone generated family of distributions : Properties and applications (2018, background): “For example, the Kummer beta-G family by Pescim et al. (2012), exponentiated generalized-G family by Cordeiro et al. (2013), Weibull-G family by Bourguignon et al. (2014), Lomax-G family by Cordeiro et al. (2014), the type I half-logistic-G family by Cordeiro et al. (2015).”
A New Weibull-G Family of Distributions (2015, methodology): “[8], exponentiated half-logistic by Cordeiro et al.”
The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling (2019, methodology): “Then, the OPL-G family can be expressed as OPL −G ( x;α, β, ψ ) = p [ OW-G ( x;α, β, ψ )] + (1 − p) [ GG-G ( x;α, β, ψ )] , (6) where p = β/ (β + 1) is the mixing proportion.”
A new family of distributions with properties, regression models and applications (2018, neutral): “k k k a θ         − Now, applying (5) for [1 log ( ; )], G x ξ − still in Equation (2), we obtain”