tpn (version 1.10)

est.tpt: 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)

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.

Arguments

y

the response vector. All the values must be positive.

x

the covariates vector.

q

quantile of the distribution to be modelled.

Author

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

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.

Examples

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