est.tpt: Parameter estimation for the tpt distribution

In tpn: Truncated Positive Normal Model and Extensions

Parameter estimation for the tpt distribution

Description

Perform the parameter estimation for the truncated positive t (tpt) distribution based on maximum likelihood estimation. Estimated errors are computed based on the hessian matrix.

Usage

est.tpt(y, x = NULL, q = 0.5)

Arguments

y	the response vector. All the values must be positive.
x	the covariates vector.
q	quantile of the distribution to be modelled.

Details

A variable have tpt distribution with parameters \sigma>0, \lambda \in R and \nu>0 if its probability density function can be written as

f(y; \sigma, \lambda, q) = \frac{t_\nu\left(\frac{y}{\sigma}-\lambda\right)}{\sigma T_\nu(\lambda)}, y>0,

where t_\nu(\cdot) and T_\nu(\cdot) denote the density and cumulative distribution functions for the standard t distribution with \nu degrees of freedom.

Value

A list with the following components

estimate	A matrix with the estimates and standard errors
logLik	log-likelihood function evaluated in the estimated parameters.
AIC	Akaike's criterion.
BIC	Schwartz's criterion.

Note

A warning is presented if the estimated hessian matrix is not invertible.

Author(s)

Gallardo, D.I. and Gomez, H.J.

Examples

set.seed(2021)
y=rtpt(n=100,sigma=10,lambda=1, nu=5)
est.tpt(y)

tpn documentation built on April 11, 2025, 5:40 p.m.