Maximum likelihood estimation and Hermite regression
Description
glm.hermite
is used to fit generalized linear models with count
responses following a Hermite distribution, specified by giving a symbolic
description of the linear predictor. A summary
method providing the
most meaningful information on the fitted model is available for objects of
class glm.hermite
.
Usage
1 
Arguments
formula 
symbolic description of the model. A typical predictor has the form

data 
an optional data frame containing the variables in the model. 
link 
character specification of link function: "log" or "identity". By default

start 
a vector containing the starting values for the parameters of the specified
model. Its default value is 
m 
value for parameter 
Value
glm.hermite
returns an object of class glm.hermite
, which is a
list including the following components:
coefs the vector of coefficients.
data an optional data frame containing the variables in the model.
loglik loglikelihood of the fitted model.
vcov covariance matrix of all coefficients in the model (derived from the Hessian of the
maxLik
output).hessHessian matrix, returned by the
maxLik
output.fitted.values the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.
wLikelihood ratio test statistic.
pvalLikelihood ratio test pvalue.
Author(s)
María Oliveira, Manuel Higueras, David Moriña and Pere Puig
References
Kemp C D, Kemp A W. Some Properties of the Hermite Distribution. Biometrika 1965;52 (34):381–394.
McKendrick A G Applications of Mathematics to Medical Problems. Proceedings of the Edinburgh Mathematical Society 1926;44:98–130.
Kemp A W, Kemp C D. An alternative derivation of the Hermite distribution. Biometrika 1966;53 (34):627–628.
Patel Y C. Even Point Estimation and Moment Estimation in Hermite Distribution. Biometrics 1976;32 (4):865–873.
Gupta R P, Jain G C. A Generalized Hermite distribution and Its Properties. SIAM Journal on Applied Mathematics 1974;27:359–363.
Bekelis, D. Convolutions of the Poisson laws in number theory. In Analytic & Probabilistic Methods in Number Theory: Proceedings of the 2nd International Conference in Honour of J. Kubilius, Lithuania 1996;4:283–296.
Zhang J, Huang H. On Nonnegative IntegerValued Lévy Processes and Applications in Probabilistic Number Theory and Inventory Policies. American Journal of Theoretical and Applied Statistics 2013;2:110–121.
Kotz S. Encyclopedia of statistical sciences. John Wiley 19821989.
Kotz S. Univariate discrete distributions. Norman L. Johnson 2005.
Puig P. (2003). Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, with an Application to Generalized Hermite Distributions. Journal of the American Statistical Association 2003; 98:687–692.
See Also
Distributions
for some other distributions,
qhermite
, phermite
, rhermite
,
hermitepackage
Examples
1 2 3 