hermite (version 1.0.1)

mle.hermite: Maximum likelihood estimation for the generalized Hermite distribution

Description

Maximum likelihood estimation for the generalized Hermite distribution and likelihood ratio test for Poisson assumption.

Usage

mle.hermite(x, a=NA, b=NA, m=NA)

Arguments

x

vector containing the sample observations.

a

initial value for the first parameter for the Hermite distribution. It's default value is NA.

b

initial value for the second parameter for the Hermite distribution. It's default value is NA.

m

Order of the generalized Hermite distribution. Its default value is NA.

Value

• A list with five elements, the first containing the estimates of parameters a and b. The second element contains the maximum likelihood value and the third element contains the Hessian matrix. The fourth element of the returned value contains the likelihood ratio test statistic $W$ and the last element is the p-value of the likelihood ratio test.

encoding

utf8

Details

If initial values are supplied they are used to obtain the maximum likelihood estimates for a and b. If no initial values are supplied, the naive estimates detailed in Puig (2003) are taken as initial values.

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, dhermite, phermite, qhermite, hermite-package

Examples

rnd <- rhermite(1000, 0.8, 0.3)