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A Look at the Burr and Related Distributions

Pandu R. Tadikamalla
International Statistical Review / Revue Internationale de Statistique
Vol. 48, No. 3 (Dec., 1980), pp. 337-344
DOI: 10.2307/1402945
Stable URL: http://www.jstor.org/stable/1402945
Page Count: 8
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A Look at the Burr and Related Distributions
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Abstract

The Burr distribution (Burr type XII), which yields a wide range of values of skewness and kurtosis, can be used to fit almost any given set of unimodal data. The Burr distribution has appeared in the literature under different names. The relationship between the Burr distribution and the various other distributions, namely, the Lomax, the Compound Weibull, the Weibull-Exponential, the logistic, the log logistic, the Weibull and the Kappa family of distributions is summarized. Also it is shown that the 'reciprocal Burr' distribution (Burr type III) covers a wider region in the (√ β 1,β 2) plane and includes all the region covered by the Burr type XII distribution. /// La distribution de Burr (type XII de Burr) dont les coefficients d'asymétrie et d'applatissement recouvrent un large champ de valeurs, peur servir à ajuster presque n'importe quel ensemble unimodal de données. La distribution de Burr est apparue dans la littérature sous des noms divers. La relation existant entre la distribution de Burr et les diverses autres distributions ainsi désignées: Lomax, Weibull-composée, Weibull-exponentielle, Logistique, Log-logistique, Weibull et Kappa, est résumée ici. On montre aussi que la distribution dite réciproque de Burr (type III de Burr) recouvre un champ plus vaste que la distribution de Burr dans le plan des coefficients de Pearson $(\sqrt{\beta _{1}},\beta _{2})$, champ renfermant en totalité celui de la distribution de type XII de Burr.

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