Gumbel distribution maximum likelihood estimation

Uses Newton-Raphson to estimate the parameters of the Gumbel distribution.

mlgumbel(x, na.rm = FALSE, sigma0 = 1,
  rel.tol = .Machine$double.eps^0.25, iterlim = 100)

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?
sigma0	An optional starting value for the `sigma` parameter.
rel.tol	Relative accuracy requested.
iterlim	A positive integer specifying the maximum number of iterations to be performed before the program is terminated.

Value

mlgumbel returns an object of class univariateML. This is a named numeric vector with maximum likelihood estimates for mu and s and the following attributes:

model

The name of the model.

density

The density associated with the estimates.

logLik

The loglikelihood at the maximum.

support

The support of the density.

n

The number of observations.

call

The call as captured my match.call

shape and sigma.

Details

For the density function of the Gumbel distribution see Gumbel.

References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 2, Chapter 22. Wiley, New York.

Examples

mlgumbel(precip)
#> Maximum likelihood estimates for the Gumbel model 
#>    mu  sigma  
#> 27.89  13.76