A guide to the Burr type XII distributions

Rodriguez, Robert N.

doi:10.1093/biomet/64.1.129

Cited by 256 publications

(100 citation statements)

References 8 publications

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“…This is one of the most versatile distributions in statistics. As shown by Rodriguez [8] and Tadikamalla [9], the Burr XII distribution contains the shape characteristics of the normal, log-normal, gamma, logistic and exponential distributions as well as a significant portion of the Pearson type I, II, V, VII, IX and XII families. It has received applications in life testing (see Wingo [10,11]) and many other areas.…”

Section: Burr Type XII Distributionmentioning

confidence: 94%

The model for fracture toughness

Nadarajah

2008

J Mech Sci Technol

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It is pointed out that the distribution introduced by Neville [1] (for modeling fracture toughness to failures) is contained by at least two families of distributions known since the 1940s. Some elementary statistical properties of these families are discussed. Six data sets on fracture toughness are used to demonstrate that these families are much better models for fracture toughness than the one introduced by Neville [1].

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Section: Burr Type XII Distributionmentioning

confidence: 94%

The model for fracture toughness

Nadarajah

2008

J Mech Sci Technol

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“…We have chosen the Burr distribution because it is one of the most versatile distributions in statistics. As shown by Rodriguez (1977) and Tadikamalla (1980), the Burr distribution contains the shape characteristics of the normal, log-normal, gamma, logistic and exponential distributions as well as a significant portion of the Pearson type I, II, V, VII, IX and XII families.…”

Section: Simulation Studymentioning

confidence: 99%

Asymptotic normality of location invariant heavy tail index estimator

Peng

Nadarajah

2009

Extremes

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Motivated by Fraga Alves (Extremes 4:199-217, 2001)'s work, a new class of location invariant Hill-type estimators for the tail index of a heavy tailed distribution is proposed in the paper. Its asymptotic behavior is derived, and the optimal choice of the sample fraction is discussed by mean squared error. Asymptotic comparisons and simulation studies are presented to show that the new estimator performs well compared to the known ones.

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“…For instance, the normal density function may be approximated as a Burr XII distribution with c = 4.85437 and k = 6.22665 and the Gamma distribution with shape parameter 16 can be approximated as a Burr XII distribution with c = 3 and k = 6, and the log-logistic distribution is a special case of the Burr XII distribution. Rodriguez [14] demonstrated that the Weibull distribution is a limiting distribution of the Burr XII distribution. Hence, the two-parameter Burr XII distribution can be used to describe the data in the real world.…”

Section: The Burr XII Distributionmentioning

confidence: 99%