Estimate inverse Gaussian model parameters by the maximum likelihood method using possibly censored data. Two different parameterizations of the inverse Gaussian distribution can be used. The corresponding code for this function as well as the manual information included here is attributed to Christophe Pouzat's STAR Package (archived 2022-05-23).
invgaussMLE(yi, ni = numeric(length(yi)) + 1,
si = numeric(length(yi)) + 1,
parameterization = "sigma2")A list of class durationFit with the following components:
the estimated parameters, a named vector.
the standard errors, a named vector.
the log likelihood at maximum.
a function returning the log of the relative likelihood function.
a function returning the opposite of the log likelihood function using the log of the parameters.
the matched call.
vector of (possibly binned) observations or a
spikeTrain object.
vector of counts for each value of yi; default: numeric(length(yi))+1.
vector of counts of uncensored observations for each
value of yi; default: numeric(length(yi))+1.
parameterization used, "sigma2"
(default) of "boundary".
Christophe Pouzat christophe.pouzat@gmail.com
The two different parameterizations of the inverse Gaussian distribution
are discussed in the manual of dinvgauss.
In the absence of censored data the ML estimates are available in
closed form (Lindsey, 2004, p 212) together with the Hessian matrix at
the MLE. In presence of censored data an initial guess for the
parameters is obtained using the uncensored data before maximizing the
likelihood function to the full data set using optim
with the BFGS method. ML
estimation is always performed with the "sigma2"
parameterization. Parameters and variance-covariance matrix are
transformed at the end if the "boundary" parameterization is
requested.
In order to ensure good behavior of the numerical optimization
routines, optimization is performed on the log of the parameters
(mu and sigma2).
Standard errors are obtained from the inverse of the observed information matrix at the MLE. They are transformed to go from the log scale used by the optimization routine, when the latter is used (ie, for censored data) to the parameterization requested.
Lindsey, J.K. (2004) Introduction to Applied Statistics: A Modelling Approach. OUP.
dinvgauss, gammaMLE, llogisMLE