The Weibull-geometric distribution

By W. Barreto‐Souza, A. de Morais, Gauss Moutinho Cordeiro. 2008

230 citations recorded by the source corpus.

For the first time, we propose the Weibull-geometric (WG) distribution which generalizes the extended exponential-geometric (EG) distribution introduced by Adamidis et al. [K. Adamidis, T. Dimitrakopoulou, and S. Loukas, On a generalization of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), pp. 259–269], the exponential-geometric distribution discussed by Adamidis and Loukas [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42] and the Weibull distribution. We derive many of its standard properties. The hazard function of the EG distribution is monotone decreasing, but the hazard function of the WG distribution can take more general forms. Unlike the Weibull distribution, the new distribution is useful for modelling unimodal failure rates. We derive the cumulative distribution and hazard functions, moments, density of order statistics and their moments. We provide expressions for the Rényi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an EM algorithm [A.P. Dempster, N.M. Laird, and D.B. Rubim, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. R. Stat. Soc. B 39 (1977), pp. 1–38; G.J. McLachlan and T. Krishnan, The EM Algorithm and Extension, Wiley, New York, 1997] is given for estimating the parameters. We obtain the observed information matrix and discuss inference issues. The flexibility and potentiality of the new distribution is illustrated by means of a real data set.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/27330398f082cb3e3828f722b3d9470cd6e93e27

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Citations in the corpus

Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data (2019, methodology): “5 Applications In this section, we fit the αPTL distribution to two real data sets and compare with the Lindley (Equation (5)), exponential (E), exponentiated logistic (EL), and Weibull distributions, whose densities are given by”
Transmuted Complementary Weibull Geometric Distribution (2014, methodology): “Tojeiro et al. (2014) introduced the complementary Weibull geometric (CWG) as a complementary distribution to the Weibull geometric (WG) model proposed by Barreto-Souza et al. (2011).”
General results for the Marshall and Olkin's family of distributions (2013, unknown): “(2005); see also Barreto-Souza et al. (2011). We obtain”
General results for the Kumaraswamy-G distribution (2012, methodology): “[16] who investigated the beta exponentiated exponential distribution.”
The beta Weibull-geometric distribution (2013, unknown): “16 by taking <inline-graphic xmlns:xlink="http://www.”
The Burr XII power series distributions: A new compounding family (2015, background): “Barreto-Souza et al. (2010) and Lu and Shi (2012) proposed the Weibull–geometric (WG) and Weibull–Poisson (WP) distributions, which naturally extend the EG and EP distributions, respectively.”
A new two parameter lifetime distribution: model and properties (2012, methodology): “[6], where the last was obtained by compounding Weibull and geometric distributions.”
A new lifetime model with decreasing failure rate (2010, methodology): “[7], where the last was obtained by compounding Weibull and geometric distributions.”
A new compounding life distribution: the Weibull–Poisson distribution (2012, unknown): “[2] introduced a Weibull-geometric (WG) distribution which generalizes the EG and Weibull distributions.”