Perform the parameter estimation for the slash truncated positive normal (stpn) discussed in Gomez, Gallardo and Santoro (2021) based on the EM algorithm. Estimated errors are computed based on the Louis method to approximate the hessian matrix.
est.stpn(y, sigma0=NULL, lambda0=NULL, q0=NULL, prec = 0.001,
max.iter = 1000)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.
initial values for the EM algorithm for sigma, lambda and q. If they are omitted, by default sigma0 is defined as the root of the mean of the y^2, lambda as 0 and q as 3.
the precision defined for each parameter. By default is 0.001.
the maximum iterations for the EM algorithm. By default is 1000.
Gallardo, D.I. and Gomez, H.J.
A variable has stpn distribution with parameters \(\sigma>0, \lambda \in\) R and \(q>0\) if its probability density function can be written as $$ f(y; \sigma, \lambda, q) = \int_0^1 t^{1/q} \sigma \phi(y t^{1/q} \sigma-\lambda)dt, y>0, $$ where \(\phi(\cdot)\) denotes the density function for the standard normal distribution.
Gomez, H., Gallardo, D.I., Santoro, K. (2021) Slash Truncation Positive Normal Distribution: with application using the EM algorithm. Symmetry, 13, 2164.
set.seed(2021)
y=rstpn(n=100,sigma=10,lambda=1,q=2)
est.stpn(y)
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