est.btpn {tpn}

Parameter estimation for the btpn model

Description

Perform the parameter estimation for the bimodal truncated positive normal (btpn) discussed in Gomez et al. (2022). Estimated errors are computed based on the hessian matrix.

Usage

est.btpn(y)

Arguments

y

the response vector. All the values must be positive.

Details

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

f(y; \sigma, \lambda, q) = \frac{\phi\left(\frac{x}{\sigma(1+\epsilon)}+\lambda\right)}{2\sigma\Phi(\lambda)}, y<0,

and

f(y; \sigma, \lambda, q) = \frac{\phi\left(\frac{x}{\sigma(1-\epsilon)}-\lambda\right)}{2\sigma\Phi(\lambda)}, y\geq 0,

where \epsilon=\eta/\sqrt{1+\eta^2} and \phi(\cdot) and \Phi(\cdot) denote the probability density function and the cumulative distribution function for the standard normal distribution, respectively.

Value

A list with the following components

estimate

A matrix with the estimates and standard errors

iter

Iterations in which the convergence were 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., Gomez, H.J. and Gomez, Y.M.

References

Gomez, H.J., Caimanque, W., Gomez, Y.M., Magalhaes, T.M., Concha, M., Gallardo, D.I. (2022) Bimodal Truncation Positive Normal Distribution. Symmetry, 14, 665.

Examples

set.seed(2021)
y=rbtpn(n=100,sigma=10,lambda=1,eta=1.5)
est.btpn(y)