dPT: The Poisson-Tweedie family of distributions

Description

Density function and random generation for the Poisson-Tweedie family of distributions.

Usage

dPT(x, mu, D, a, tol = 1e-15)
rPT(n, mu, D, a, max = 10*sqrt(mu*D), tol = 1e-4)

Arguments

an object of class 'mlePT' or a non-negative vector containing the integers in which the distribution should be evaluated.

numeric positive scalar giving the mean of the distribution.

numeric positive scalar giving the dispersion of the distribution.

numeric scalar smaller than 1 giving the shape parameter of the distribution.

tol

numeric scalar giving the tolerance.

integer scalar giving number of random values to return.

max

numeric scalar containing the maximum number of counts to be used in the sampling process.

Value

If 'x' is of class 'mlePT', 'dPT' will return the Poisson-Tweedie distribution with parameters equal to the ones estimated by 'mlePoissonTweedie' evaluated on the data that was used to estimate the parameters. If 'x' is a numeric vector, 'dPT' will return the density of the specified Poisson-Tweedie distribution evaluated on 'x'.'rPT' generates random deviates.

References

Esnaola M, Puig P, Gonzalez D, Castelo R and Gonzalez JR (2013). A flexible count data model to fit the wide diversity of expression profiles arising from extensively replicated RNA-seq experiments. BMC Bioinformatics 14: 254 A.H. El-Shaarawi, R. Zhu, H. Joe (2010). Modelling species abundance using the Poisson-Tweedie family. Environmetrics 22, pages 152-164. P. Hougaard, M.L. Ting Lee, and G.A. Whitmore (1997). Analysis of overdispersed count data by mixtures of poisson variables and poisson processes. Biometrics 53, pages 1225-1238.

Examples

Run this code

# To compute the density function in 1:100 of the Polya-Aeppli
# distribution with mean = 20 and dispersion = 5
dPT(x = 1:100, mu = 20, D = 5, a = -1)

# To generate 100 random counts of the same distribution with same
# parameters
rPT(n = 100, mu = 20, D = 5, a = -1)