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.
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.
Martin Becker martin.becker@mx.uni-saarland.de and Stefan Klößner S.Kloessner@mx.uni-saarland.de
Maintainer: Martin Becker martin.becker@mx.uni-saarland.de
[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
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.
## see documentation of individual functions
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