nsRFA (version 0.5-8)

MLlaio2004: 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 "GUMBEL", Generalized Extreme Value "GEV", Pearson type III "P3" 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

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.

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="P3")
ML_estimation (sm, dist="P3")
Fx (sm, c(-1.6,0.78,2.8), dist="P3")