Document Type

Article

Source Publication Title

ISRN Applied Mathematics

First Page

1

Last Page

14

DOI

http://dx.doi.org/10.1155/2013/191604

Abstract

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate ??-moments and the ??- correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of ??-skew, ??-kurtosis, and ??-correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that ??-moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of ??-skew, ??-kurtosis, and ??-correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.

Disciplines

Curriculum and Instruction | Education

Publication Date

1-1-2013

Language

English

License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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