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.
est.btpn(y)A list with the following components
A matrix with the estimates and standard errors
Iterations in which the convergence were attached.
log-likelihood function evaluated in the estimated parameters.
Akaike's criterion.
Schwartz's criterion.
the response vector. All the values must be positive.
Gallardo, D.I., Gomez, H.J. and Gomez, Y.M.
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.
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.
set.seed(2021)
y=rbtpn(n=100,sigma=10,lambda=1,eta=1.5)
est.btpn(y)
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