glm.hermite: Maximum likelihood estimation and Hermite regression

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/glm.hermite.R

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
  glm.hermite(formula, data, link="log", start=NULL, m = NULL)

Arguments

formula

symbolic description of the model. A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response.

data

an optional data frame containing the variables in the model.

link

character specification of link function: "log" or "identity". By default link="log".

start

a vector containing the starting values for the parameters of the specified model. Its default value is NULL.

m

value for parameter m. Its default value is NULL, and in that case it will be estimated inside the function.

Value

glm.hermite returns an object of class glm.hermite, which is a list including the following components:

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 (3-4):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 (3-4):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 Integer-Valued 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 1982-1989.

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, hermite-package

Examples

1
2
3
data <- c(rep(0,122), rep(1,40), rep(2,14), rep(3,16), rep(4,6), rep(5,2))
mle1 <- glm.hermite(data~1, link="log", start=NULL, m=3)
mle1

Example output

Loading required package: maxLik
Loading required package: miscTools

Please cite the 'maxLik' package as:
Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1.

If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site:
https://r-forge.r-project.org/projects/maxlik/
$coefs
     (Intercept) dispersion.index            order 
      -0.2877067        1.8903869        3.0000000 

$loglik
[1] -235.8354

$vcov
            [,1]        [,2]
[1,] 0.012594266 0.006583366
[2,] 0.006583366 0.017228285

$hess
          [,1]      [,2]
[1,] -99.22019  37.91456
[2,]  37.91456 -72.53220

$fitted.values
  [1] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
  [8] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [15] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [22] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [29] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [36] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [43] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [50] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [57] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [64] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [71] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [78] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [85] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [92] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
 [99] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[106] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[113] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[120] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[127] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[134] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[141] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[148] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[155] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[162] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[169] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[176] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[183] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[190] 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815 0.7499815
[197] 0.7499815 0.7499815 0.7499815 0.7499815

$w
[1] 48.66494

$pval
[1] 1.518234e-12

attr(,"class")
[1] "glm.hermite"
attr(,"Call")
glm.hermite(formula = data ~ 1, link = "log", start = NULL, m = 3)
attr(,"x")
    (Intercept)
1             1
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attr(,"x")attr(,"assign")
[1] 0

hermite documentation built on May 30, 2017, 3:07 a.m.