Distribution function for the generalized Hermite distribution

Description

Distribution function for the generalized Hermite distribution with parameters a, b and m.

Usage

1
  phermite(q, a, b, m=2, lower.tail=TRUE)

Arguments

q

vector of non-negative integer quantiles.

a

first parameter for the Hermite distribution.

b

second parameter for the Hermite distribution.

m

degree of the generalized Hermite distribution. Its default value is 2, corresponding to the standard Hermite distribution.

lower.tail

logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].

Value

Probability for a generalized Hermite random varible with parameters a, b and m to be lower (or greater) than q.

Author(s)

David Moriña, Manuel Higueras, Pedro Puig and María Oliveira

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, qhermite, rhermite, hermite-package, glm.hermite

Examples

1
d <- phermite(4, 0.8, 0.3, m=3)