PearsonDS: Pearson Distribution System

In PearsonDS: Pearson Distribution System

Pearson Distribution System

Description

Implementation of the d,p,q,r function family, calculation of moments, and fitting via (empirical) moment matching as well as maximum likelihood method for the Pearson distribution system.

Warning

If at all possible, package gsl should be installed. In this case, the functions for Pearson type IV distributions make use of lngamma_complex (see Gamma). If package gsl is not installed, some calculations for Pearson type IV distributions with (more or less) extreme parameters (ie, big nu and/or m) may slow down by factors of more than 1000.

Author(s)

Martin Becker [e-mail] and Stefan Klößner [e-mail]

Maintainer: Martin Becker [e-mail]

References

[1] Abramowitz, M. and I. A. Stegun (1972) Handbook of mathematical functions, National Bureau of Standards, Applied Mathematics Series - 55, Tenth Printing, Washington D.C.

[2] Heinrich, J. (2004) A Guide to the Pearson Type IV Distribution, Univ. Pennsylvania, Philadelphia, Tech. Rep. CDF/Memo/Statistics/Public/6820 http://www-cdf.fnal.gov/physics/statistics/notes/cdf6820_pearson4.pdf

[3] Hida, Y., X. S. Li and D. H. Bailey (2000) Algorithms for quad-double precision floating point arithmetic, Lawrence Berkeley National Laboratory. Paper LBNL-48597.

[4] Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 1, Wiley Series in Probability and Mathematical Statistics, Wiley

[5] Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 2, Wiley Series in Probability and Mathematical Statistics, Wiley

[6] Willink, R. (2008) A Closed-form Expression for the Pearson Type IV Distribution Function, Aust. N. Z. J. Stat. 50 (2), pp. 199-205

See Also

Pearson for d,p,q,r function family for Pearson distributions, pearsonFitM and pearsonFitML for fitting Pearson distributions, pearsonMSC for model selection, pearsonMoments for calculation of (first four) moments.

Examples

## see documentation of individual functions

PearsonDS documentation built on April 3, 2025, 5:37 p.m.