dctp: Probability Mass Function of the CTP Distribution

In zmctp: Zero-Modified Complex 'Tri-Parametric' Pearson Distribution for Overdispersed Count Data

Probability Mass Function of the CTP Distribution

Description

Evaluates the probability mass function of the Complex TriParametric Pearson (CTP) distribution for nonnegative integer values.

The pmf is

p(x) = p(0)\frac{(a+ib)_x(a-ib)_x}{(\gamma)_x x!}, \quad x=0,1,\dots

and satisfies the recurrence

\frac{p(x+1)}{p(x)} = \frac{(a+x)^2+b^2}{(\gamma+x)(x+1)}.

Usage

dctp(x, a, b, gama, log = FALSE)

Arguments

x	Vector of nonnegative integers.
a	Parameter a.
b	Parameter b (must satisfy b >= 0).
gama	Parameter gamma.
log	Logical; if TRUE, returns log-probabilities.

Value

A numeric vector of probabilities.

Examples

dctp(0:5, a = 1, b = 0.5, gama = 6)

zmctp documentation built on Sept. 20, 2026, 5:07 p.m.