# texmexFamily: Create families of distributions In texmex: Statistical Modelling of Extreme Values

## Description

Create families of distributions for use with extreme value modelling.

## Usage

 1 2 3 4 5 6 7 8 texmexFamily(name, log.lik, param, info = NULL, sandwich = NULL, start = NULL, resid = NULL, rl, delta, endpoint, density, rng, prob, quant) ## S3 method for class 'texmexFamily' print(x,...) ## S3 method for class 'texmexFamily' summary(object,...) ## S3 method for class 'summary.texmexFamily' print(x,...)

## Arguments

 name The name of the distribution. log.lik The distribution's log-likelihood function. param The names of the parameters in the model. info Function to compute the information matrix. If not provided, the modelling functions will work with a numerical approximation. sandwich Function to compute the filling in the Huber sandwich estimator of the covariance matrix of parameter estimates, used for dependent data. Only implemented in family gpd. start Function to compute starting parameters for the model. If not provided, the modelling functions will try to guess. resid Function to compute residuals for the model. rl Function to compute return levels. delta Function to compute adjustments for covariance for return levels. endpoint Function to compute the upper or lower endpoint of the fitted distribution. density Function to compute the density. rng Function for random number generation. prob Function to compute cumulative probabilities. quant Function to compute quantiles. ... Additional arguments to the print and summary methods. x, object An object of class 'texmexFamily'.

## Details

The density, rng, prob and quant functions can be simple wrappers for the usual d, r, p and q functions. They should take a matrix with number of columns equal to the number of parameters, and a fitted model object even if the model object is not used by the function.

Examples of "texmexFamily" objects are gpd, gev, weibull, gumbel and egp3. Take a look at those objects to see how the functions should be constructed.

The functions are used by the modelling functions to create diagnostic plots, predictions, etc..

## Value

A object of class "texmexFamily", which is essentially a list containing the input arguments. If info, sandwich, start, resid are not provided, they default to NULL.

## Note

The gpd, gev, weibull, gumbel and egp3 families are provided. The evm function defaults to using the gpd family.

Harry Southworth