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.
est.fts(y, dist="norm")A list with the following components
A matrix with the estimates and standard errors
distribution specified
the code related to the convergence for the optim function. 0 if the convergence was attached.
log-likelihood function evaluated in the estimated parameters.
Akaike's criterion.
Schwartz's criterion.
the response vector. All the values must be positive.
standard symmetrical distribution. Avaliable options: norm (default), logis, cauchy and laplace.
Gallardo, D.I. and Gomez, H.J.
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).
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.
set.seed(2021)
y=rfts(n=100,sigma=10,lambda=1,dist="logis")
est.fts(y,dist="logis")
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