est.fts {tpn}

Parameter estimation for the ftp class of distributions

Description

Perform the parameter estimation for the Flexible truncated positive (fts) class discussed in Gomez et al. (2022) based on maximum likelihood estimation. Estimated errors are computed based on the hessian matrix.

Usage

est.fts(y, dist="norm")

Arguments

y

the response vector. All the values must be positive.

dist

standard symmetrical distribution. Avaliable options: norm (default), logis, cauchy and laplace.

Details

A variable has fts distribution with parameters \sigma>0 and \lambda \in R if its probability density function can be written as

f(y; \sigma, \lambda, q) = \frac{g_0(\frac{y}{\sigma}-\lambda)}{\sigma G_0(\lambda)}, y>0,

where g_0(\cdot) and G_0(\cdot) denote the pdf and cdf for the specified distribution. The case where g_0(\cdot) and G_0(\cdot) are from the standard normal model is known as the truncated positive normal model discussed in Gomez et al. (2018).

Value

A list with the following components

estimate

A matrix with the estimates and standard errors

dist

distribution specified

conv

the code related to the convergence for the optim function. 0 if the convergence was attached.

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.

References

Gomez, H.J., Gomez, H.W., Santoro, K.I., Venegas, O., Gallardo, D.I. (2022). A Family of Truncation Positive Distributions. Submitted.

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=rfts(n=100,sigma=10,lambda=1,dist="logis")
est.fts(y,dist="logis")