# Distribution function for the generalized Hermite distribution

### Description

Distribution function for the generalized Hermite distribution with
parameters `a`

, `b`

and `m`

.

### Usage

1 |

### 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 |

`lower.tail` |
logical; if TRUE (default), probabilities are |

### 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)
``` |

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