The Conway-Maxwell-Poisson (COM-Poisson) Distribution.

Source: R/comp_distribution.R

Density, distribution function, quantile function and random generation for the Conway-Maxwell-Poisson distribution with parameter mu and nu

dcomp(
  x,
  mu,
  nu = 1,
  lambda,
  log.p = FALSE,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  summax
)

pcomp(
  q,
  mu,
  nu = 1,
  lambda,
  lower.tail = TRUE,
  log.p = FALSE,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  summax
)

qcomp(
  p,
  mu,
  nu = 1,
  lambda,
  lower.tail = TRUE,
  log.p = FALSE,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  summax
)

rcomp(
  n,
  mu,
  nu = 1,
  lambda,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  summax
)

Arguments

x, q

vector of quantiles

mu, nu

mean and dispersion parameters. Must be strictly positive.

lambda

an alternative way than mu to parametrized the distribution. Must be strictly positive

log.p

logical; if TRUE, probabilities/densities \(p\) are returned as \(log(p)\).

lambdalb, lambdaub

numeric: the lower and upper end points for the interval to be searched for lambda(s).

maxlambdaiter

numeric: the maximum number of iterations allowed to solve for lambda(s).

tol

numeric: the convergence threshold. A lambda is said to satisfy the mean constraint if the absolute difference between the calculated mean and mu is less than tol.

summax

numeric; maximum number of terms to be considered in the truncated sum.

lower.tail

logical; if TRUE (default), probabilities are \(P(X \le x)\), otherwise, \(P(X>x)\).

p

vector of probabilities

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Value

dcomp gives the density, pcomp gives the distribution function, qcomp gives the quantile function, and rcomp generates random deviates. Invalid arguments will result in return value NaN, with a warning. The length of the results is determined by n for rcomp, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the results. Only the first argument of the logical arguments are used.

Examples

dcomp(0:5, mu = 2, nu = 1.2)
#> [1] 0.11374731 0.27609781 0.29170831 0.18946331 0.08713145 0.03065722
pcomp(5, mu = 2, nu = 1.2)
#> [1] 0.9888054
p <- (1:9) / 10
qcomp(p, mu = 2, nu = 0.8)
#> [1] 0 1 1 1 2 2 3 3 4
rcomp(10, mu = 2, nu = 0.7)
#>  [1] 3 0 2 5 7 1 0 4 7 7