qhermite: Quantile function for the generalized Hermite distribution

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

View source: R/qhermite.R


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


  qhermite(p, a, b, m=2, lower.tail=TRUE)



vector of probabilities.


first parameter for the Hermite distribution.


second parameter for the Hermite distribution.


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


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


The smallest integer x such that P(X ≤ x) ≥ p (or such that P(X ≤ x) ≥ 1-p if lower.tail is set to FALSE), where X is a generalized Hermite random variable with parameters a, b and m.


David Moriña, Manuel Higueras, Pedro Puig and María Oliveira


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, rhermite, hermite-package, glm.hermite


d <- qhermite(0.9999987, 0.8, 0.3, m=3)

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

Search within the hermite package
Search all R packages, documentation and source code