pearsonMoments {PearsonDS}

Moments of Pearson Distribution

Description

Calculates the first four moments (mean, variance, skewness, kurtosis) of a Pearson distribution.

Usage

pearsonMoments(params, moments)

Arguments

params

vector/list of parameters for Pearson distribution. First entry gives type of distribution (0 for type 0, 1 for type I, ..., 7 for type VII), remaining entries give distribution parameters (depending on distribution type).

moments

optional vector/list of mean, variance, skewness, kurtosis (not excess kurtosis). Overrides params with corresponding pearson distribution, if given.

Value

Named vector of length 4 containing mean, variance, skewness and kurtosis (in this order).

Note

Optional parameter moments is merely for testing purposes. Of course, pearsonMoments should reproduce its input (when neglecting rounding errors) if moments is given.

kurtosis is the kurtosis of the distribution, not the excess kurtosis!

Author(s)

Martin Becker [e-mail]

References

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

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

See Also

PearsonDS-package, Pearson0, PearsonI, PearsonII, PearsonIII, PearsonIV, PearsonV, PearsonVI, PearsonVII,

Examples

## Define moments of distribution
moments <- c(mean=1,variance=2,skewness=1,kurtosis=5)
## Are the moments reproduced?
pearsonMoments(moments=moments)