5.40 get_marginal_distr_pearson

Function File: [r type ] = get_marginal_distr_pearson (mu, sigma, skew, kurt, Z)

Compute a marginal distribution for given set of uniform random variables with given mean, standard deviation skewness and kurtosis. The mapping is done via the Pearson distribution family.
The implementation is based on the R package ’PearsonDS: Pearson Distribution System’ and the function ’pearsonFitM’ by
Martin Becker and Stefan Kloessner (2013)
R package version 0.97.
URL: http://CRAN.R-project.org/package=PearsonDS
licensed under the GPL >= 2.0
Input and output variables:

• mu: mean of marginal distribution (scalar)
• sigma: standard deviation of marginal distribution (scalar)
• skew: skewness of marginal distribution (scalar)
• kurt: kurtosis of marginal distribution (scalar)
• Z: uniform distributed random variables (Nx1 vector)
• r: OUTPUT: Nx1 vector with random variables distributed according to Pearson type (vector)
• type: OUTPUT: Pearson distribution type (I - VII) (scalar)

The marginal distribution type is chosen according to the input parameters out of the Pearson Type I-VII distribution family:

• Type 0 = normal distribution
• Type I = generalization of beta distribution
• Type II = symmetric beta distribution
• Type III = gamma or chi-squared distribution
• Type IV = special distribution, not related to any other distribution
• Type V = inverse gamma distribution
• Type VI = beta-prime or F distribution
• Type VII = Student’s t distribution

See also: discount_factor.