A Look at the Burr and Related Distributions

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 (V•,f fi2) plane and includes all the region covered by the Burr type XII distribution.

Consequences to flood management of using different probability distributions to estimate extreme rainfall

“…Johnson et al, 1994;Forbes et al, 2011) or in focused articles (e.g. Burr, 1942;Tadikamalla, 1980). The goodness-of-fit was measured using the Kolmogorov-Smirnov (K-S) and the Anderson-Darling (A-D) tests.…”

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

“…For example, Balkema and de Haan (1974) show that it arises as the limit distribution of residual lifetime at great age; Dubey (1970) shows that it can be derived as a special case of a particular compound gamma distribution; and Tadikamalla (1980) relates the Lomax distribution to the Burr family of distributions. On the other hand, the Lomax distribution has itself been used as the basis for several generalizations.…”

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

“…Of the 12 distribution functions introduced by Burr (1942), the Burr Type III and Type XII distributions have received much of the attention because these include several families of non-normal distributions (e.g., the Gamma distribution) with varying degrees of skew and kurtosis (Burr, 1973;Headrick et al, 2010;Rodriguez, 1977;Tadikamalla, 1980). These distributions have been used primarily for statistical modeling of events arising in a variety of applied mathematical contexts.…”

“…Parameter c is negative for Type III and positive for Type XII distribution, whereas parameter k is positive for both Type III and Type XII distributions . The scale parameter that is typically used to characterize Burr distributions (e.g., Gove et al, 2008;Lindsay et al, 1996;Tadikamalla, 1980) is assumed to be one in (1) and (2) as in Burr (1942). The quantile functions associated with (1) and (2) are expressed as Eqs.…”