The beta generalized exponential distribution

By W. Barreto‐Souza, Alessandro Henrique da Silva Santos, Gauss Moutinho Cordeiro. 2008

277 citations recorded by the source corpus.

A new distribution called the beta generalized exponential distribution is proposed. It includes the beta exponential and generalized exponential (GE) distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. The density function can be expressed as a mixture of generalized exponential densities. This is important to obtain some mathematical properties of the new distribution in terms of the corresponding properties of the GE distribution. We derive the moment generating function (mgf) and the moments, thus generalizing some results in the literature. Expressions for the density, mgf and moments of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and obtain the information matrix that is easily numerically determined. We observe in one application to a real skewed data set that this model is quite flexible and can be used effectively in analyzing positive data in place of the beta exponential and GE distributions.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e75696dab756f0fc703649e7043727d16ff24d2e

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In Management Science and Operations Research

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Citations in the corpus

General results for the beta-modified Weibull distribution (2011, unknown): “[22] provided closed form expressions for the”
THE BETA GENERALIZED PARETO DISTRIBUTION (2011, background): “[19] introduce the four parameter beta generalized exponential distribution as a generalization of some well-”
A new class of generalized Lindley distributions with applications (2015, methodology): “[12] proposed the beta-Gumbel, beta-Frechet, beta-exponential (BE) and beta-exponentiated exponential distributions by taking the baseline cdf G(x) in Equation (5) above to be the cdf of the Gumbel, Frechet, exponential and exponentiated exponential distributions, respectively.”
Exponentiated $T$-$X$ Family of Distributions with Some Applications (2013, methodology): “The MLEs of the beta exponential distribution and beta generalized exponential distribution (BGED) are taken from Barreto-Souza et al. (2010), and the MLEs of beta Fréchet distribution (BFD) are from Barreto-Souza et al. (2011).”
Marshall-Olkin generalized exponential distribution (2015, unknown): “Note that the density g(x;α, λ, θ) can be represented in the generalized mixture form of beta generalized exponential probability density functions, Barreto-Souza et al. (2010), as g(x;α, λ, θ) = θ ∞∑ k=0 (1− θ)kfBGE(1,k+1,λ,α)(x).”
A New Extension of Generalized Exponential Distribution with Application to Ozone Data (2017, background): “© 2017 International Ozone Association Barreto-Souza, Santos, and Cordeiro (2010) studied the beta GE distribution, Merovci (2013) proposed the transmuted GE distribution, Tahir et al. (2015) introduced the Odd GE family of distributions and Ristić and Kundu (2015) studied Marshall-Olkin GE…”
The Beta-Dagum Distribution: Definition and Properties (2013, methodology): “In order to show the usefulness of the BDa distribution in different contexts, we consider a second data set, already used in Barreto-Souza et al. (2010). In this article, the authors fit the Beta Generalized Exponential (BGE) distribution to these data.”
The beta Weibull-geometric distribution (2013, methodology): “[13] with G(x; θ) in Equation (1) to be the cdf of the generalized exponential (GE) distribution of Gupta and Kundu [4], and the beta modified Weibull (MW) distribution introduced by Silva et al.”
A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data (2016, unknown): “[16] proposed the beta-Gumbel, beta-Frechet, beta-exponential (BE), beta-exponentiated exponential (BEE) distributions, respectively.”