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
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Pant, Mohan and Headrick, Todd C., "A Method for Simulating Burr Type III and Type XII Distributions through Moments and Correlations" (2013). Curriculum and Instruction Faculty Publications. 45.
https://mavmatrix.uta.edu/curriculuminstruction_facpubs/45