Gumbel distribution maximum likelihood estimation

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

Usage

mlgumbel(x, na.rm = FALSE, ...)

Arguments

x

a (non-empty) numeric vector of data values.

na.rm

logical. Should missing values be removed?

...

sigma0 is an optional starting value defaulting to 1. rel.tol is the relative accuracy requested, defaults to .Machine$double.eps^0.25. iterlim is a positive integer specifying the maximum number of iterations to be performed before the program is terminated (defaults to 100).

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.

See also

Gumbel for the Gumbel density.

Examples

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