mleigt {ig}R Documentation

MLE of the parameters of the IGTD

Description

The function mleigt gives the maximum likelihood estimates (MLE) of the parameters mu and lambda of the IGTD generated from the kernels: Laplace, logistic and normal (classical case) based on a sample of observations based on this distribution.

Usage

mleigt(x, kernel = "normal")

Arguments

x Vector of observations.
kernel Kernel of the pdf of the associated symmetrical distribution by means of which the IGTD is obtained. The kernels: "laplace", "logistic" and "normal" are available.

Details

The MLEs of the parameters mu and lambda of the classical IG distribution are obtained using the analytical expressions of these estimators. In the case of the IGTD generated from the kernels: Laplace, logistic and normal, the MLEs of the parameters mu and lambda must be obtained using numerical procedure already implmented in R.

Value

mleigt() computes MLEs for the parameters of the IGTD generated from the kernels: Laplace, logistic and normal giving results according to the following list:

muEstimate Returns the value of the MLE of mu.
lambdaEstimate Returns the value of the MLE of lambda.
loglikelihood Returns the value of the IGTD loglikelihood.

Author(s)

Víctor Leiva <victor.leiva@uv.cl; victor.leiva@yahoo.com>,
Hugo Hernández <hugo.hernandez.p@gmail.com> and
Antonio Sanhueza <asanhueza@ufro.cl>.

References

Sanhueza, A., Leiva, V., Balakrishnan, N. (2008). A new class of inverse Gaussian type distributions. Metrika (in press).

Examples

## Generates a sample from the IGTD with t kernel
x <- rigt(300, mu = 1.0, lambda = 1.0, nu = 5, kernel = "normal")

## Computes the likelihood for a sample x from the IGTD with normal kernel
mleigt(x)

[Package ig version 1.2 Index]