tpn (version 1.8)

est.tpn: Parameter estimation for the tpn

Description

Perform the parameter estimation for the truncated positive normal (tpn) discussed in Gomez et al. (2018) based on maximum likelihood estimation. Estimated errors are computed based on the hessian matrix.

Usage

est.tpn(y)

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.

Author

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

Details

A variable have tpn distribution with parameters \(\sigma>0\) and \(\lambda \in\) R if its probability density function can be written as $$ f(y; \sigma, \lambda, q) = \frac{\phi\left(\frac{y}{\sigma}-\lambda\right)}{\sigma \Phi(\lambda)}, y>0, $$ where \(\phi(\cdot)\) and \(\Phi(\cdot)\) denote the density and cumultative distribution functions for the standard normal distribution.

References

Gomez, H.J., Olmos, N.M., Varela, H., Bolfarine, H. (2018). Inference for a truncated positive normal distribution. Applied Mathemetical Journal of Chinese Universities, 33, 163-176.

Examples

set.seed(2021)
y=rtpn(n=100,sigma=10,lambda=1)
est.tpn(y)