hermite (version 1.1.2)

qhermite: Quantile function for the generalized Hermite distribution

Description

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

Usage

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

Arguments

p

vector of probabilities.

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 \(P[X \le x]\), otherwise, \(P[X > x]\).

Value

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

References

Kemp C D, Kemp A W. Some Properties of the Hermite Distribution. Biometrika 1965;52 (3-4):381<U+2013>394.

McKendrick A G Applications of Mathematics to Medical Problems. Proceedings of the Edinburgh Mathematical Society 1926;44:98<U+2013>130.

Kemp A W, Kemp C D. An alternative derivation of the Hermite distribution. Biometrika 1966;53 (3-4):627<U+2013>628.

Patel Y C. Even Point Estimation and Moment Estimation in Hermite Distribution. Biometrics 1976;32 (4):865<U+2013>873.

Gupta R P, Jain G C. A Generalized Hermite distribution and Its Properties. SIAM Journal on Applied Mathematics 1974;27:359<U+2013>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<U+2013>296.

Zhang J, Huang H. On Nonnegative Integer-Valued L<U+00E9>vy Processes and Applications in Probabilistic Number Theory and Inventory Policies. American Journal of Theoretical and Applied Statistics 2013;2:110<U+2013>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<U+2013>692.

See Also

Distributions for some other distributions, dhermite, phermite, rhermite, hermite-package, glm.hermite

Examples

# NOT RUN {
d <- qhermite(0.9999987, 0.8, 0.3, m=3)
# }