MLlaio2004 {nsRFA}R Documentation

Maximum likelihood parameters estimation

Description

Maximum Likelihood estimation of parameters for extreme-value distributions, from Laio (2004).

Usage

 ML_estimation (x, dist="NORM")
 moment_estimation (x, dist="NORM")
 logLgumb (T, x)
 logLgev (T, x)
 logLgam (T1, x)
 sample_generator (n, T, dist="NORM")

Arguments

x data sample
dist distribution: normal "NORM", Gumbel "EV1", Generalized Extreme Value "GEV", Pearson type III "GAM" and, only for sample_generator, Exponential EXP
T parameters (position, scale, shape, ...)
T1 position parameter of the Gamma (Pearson type III) distribution
n sample length

Details

Value

ML_estimation estimate the parameters of the distribution dist from a sample x using the maximum likelihood approach.
moment_estimation estimate the parameters of the distribution dist from a sample x using the moment method.
logLgumb is the negative log-likelihood function for the Gumbel distribution.
logLgev is the negative log-likelihood function for the Generalized Extreme Value distribution.
logLgam is the negative log-likelihood function for the Pearson type III distribution.
sample_generator generates a sample of length n from the distribution dist with parameters T.

Author(s)

Alberto Viglione, e-mail: alviglio@tiscali.it.

References

Laio, F., Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters, Water Resour. Res., 40, W09308, doi:10.1029/2004WR003204.

See Also

GOFlaio2004.

Examples

sm <- sample_generator(100, c(0,1), dist="EV1")
moment_estimation (sm, dist="GEV")
ML_estimation (sm, dist="GEV")
Fx (sm, c(-0.051,0.97,-0.024), dist="GEV")
sample_generator (100, c(-0.051,0.97,-0.024), dist="GEV")

moment_estimation (sm, dist="GAM")
ML_estimation (sm, dist="GAM")
Fx (sm, c(-1.6,0.78,2.8), dist="GAM")


[Package nsRFA version 0.3-6 Index]