Conway–Maxwell–Poisson distribution functions

Density, distribution, quantile, and random generation for the COM-Poisson with rate lambda (or mean mu) and dispersion nu (nu > 1 underdispersed, nu = 1 Poisson, nu < 1 overdispersed). Complements the estimators count_reg(..., family = "compois") (rate parameterization) and count_reg(..., family = "mpcmp") (mean parameterization).

Usage

dcompois(x, lambda, nu, log = FALSE, mu = NULL)

pcompois(q, lambda, nu, lower.tail = TRUE, log.p = FALSE, mu = NULL)

qcompois(p, lambda, nu, lower.tail = TRUE, log.p = FALSE, mu = NULL)

rcompois(n, lambda, nu, mu = NULL)

Arguments

x, q

Vector of quantiles (non-negative integers).

lambda

Rate parameter (scalar or vector, recycled). Give mu instead to specify the distribution by its mean.

nu

Dispersion parameter (scalar).

log, log.p

Return log probabilities.

mu

Optional mean (scalar or vector, recycled); when supplied, the rate lambda solving \(\mathrm{E}(Y) = \mu\) is found numerically (Huang's 2017 mean parameterization, the one count_reg(family = "mpcmp") fits) and lambda is ignored.

lower.tail

If TRUE (default), \(P(X \le x)\).

p

Vector of probabilities.

n

Number of draws.

Value

dcompois a density, pcompois a CDF, qcompois a quantile, rcompois a numeric vector of count draws. A rate whose normalizing sum the 100,000-term cap would truncate (a mean of order \(10^5\) or more) gives NA.

Examples

dcompois(0:5, lambda = 3, nu = 1.5)
#> [1] 0.10062763 0.30188288 0.32019515 0.18486475 0.06932428 0.01860166
mean(rcompois(1000, lambda = 3, nu = 1.5))
#> [1] 1.881