Some Results for Beta Fréchet Distribution

By W. Barreto‐Souza, Gauss Moutinho Cordeiro, Alexandre B. Simas. 2008

125 citations recorded by the source corpus.

Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they did not investigate the moments and the order statistics. In this article, the BF density function and the density function of the order statistics are expressed as linear combinations of Fréchet density functions. This is important to obtain some mathematical properties of the BF distribution in terms of the corresponding properties of the Fréchet distribution. We derive explicit expansions for the ordinary moments and L-moments and obtain the order statistics and their moments. We also discuss maximum likelihood estimation and calculate the information matrix which was not given in the literature. The information matrix is numerically determined. The usefulness of the BF distribution is illustrated through two applications to real data sets.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ae683cc60627cff34bfb43d9175d38faa1b81b6b

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Citations in the corpus

Generalized beta-generated distributions (2012, unknown): “BG distributions have been studied by Nadarajah and Kotz (2004, 2005), Akinsete et al. (2008), Zografos and Balakrishnan (2009) and Barreto-Souza et al. (2010).”
The Weibull Fréchet distribution and its applications (2016, background): “[4] studied the beta Fr, Mahmoud and Mandouh [11] proposed the transmuted Fr, Krishna et al.”
The Beta Exponential Fréchet Distribution with Applications (2017, background): “…available in the literature, such as the exponentiated Fréchet (EFr) (Nadarajah and Kotz, 2003), beta Fréchet (BFr) (Nadarajah and Gupta, 2004 and Barreto-Souza et al., 2011), transmuted Fréchet (TFr) (Mahmoud and Mandouh, 2013), gamma extended Fréchet (GEFr) (Silva et al., 2013),…”
The Kumaraswamy Marshal-Olkin family of distributions (2015, methodology): “In the second application, we compare the KwMO-Fr model with other comparative models: the beta-Fréchet (BFr) [39], the exponentiated-Fréchet (EFr) [40], the Marshall-Olkin extended Fréchet (MOFr) [41] and the Fréchet (Fr).”
On Six-Parameter Frechet Distribution: Properties and Applications (2016, methodology): “Further, we demonstrate that the proposed model provides a significant improvement compared to some existing lifetime models and it is also a competitive model to the gamma extended Fréchet (da Silva et al., 2013) and beta Fréchet (Barreto-Souza et al., 2011) distributions.”
The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications (2015, background): “For example, Nadarajah and Kotz (2003) studied the exponentiated Fréchet (EFr), Nadarajah and Gupta (2004) and Barreto-Souza et al. (2011) independently introduced the beta Fréchet (BFr), Mahmoud and Mandouh (2013) proposed the transmuted Fréchet (TFr), Silva et al. (2013) proposed the gamma…”
Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing (2020, background): “Competitive Models (Abbreviation) Author(s) Kumaraswamy Fréchet (Kum-F) [26] Transmuted Fréchet (T-F) [27,28] Exponentiated Fréchet (EF) [5,28] Beta Fréchet (B-F) [29] Marshal–Olkin-Fréchet (MO-F) [9] McDonald Fréchet (Mc-F) [30] odd log-logistic inverse Rayleigh (OLL-IR) [13] Fréchet (F) [1] odd lo”
Exponentiated $T$-$X$ Family of Distributions with Some Applications (2013, methodology): “Barreto-Souza et al. (2010) applied the beta generalized exponential distribution to fit the data and Barreto-Souza et al.”