dgenpois {HMMpa} | R Documentation |
Density, distribution function and random generation function for the generalized Poisson distribution.
dgenpois(x, lambda1, lambda2)
pgenpois(q, lambda1, lambda2)
rgenpois(n, lambda1, lambda2)
x |
a vector object of (non-negative integer) quantiles. |
q |
a numeric value. |
n |
number of random values to return. |
lambda1 |
a single numeric value for parameter |
lambda2 |
a single numeric value for parameter |
The generalized Poisson distribution has the density
p(x) = \lambda_1 (\lambda_1 + \lambda_2 \cdot x)^{x-1} \frac{ \exp(-\lambda_1-\lambda_2 \cdot x) )}{x!}
for x = 0,1,2,\ldots
,b
with \mbox{E}(X)=\frac{\lambda_1}{1-\lambda_2}
and variance \mbox{var}(X)=\frac{\lambda_1}{(1-\lambda_2)^3}
.
dgenpois
gives the density, pgenpois
gives the distribution function and rgenpois
generates random deviates.
Based on Joe and Zhu (2005). Implementation by Vitali Witowski (2013).
Joe, H., Zhu, R. (2005). Generalized poisson distribution: the property of mixture of poisson and comparison with negative binomial distribution. Biometrical Journal 47(2):219–229.
Distributions for other standard distributions, including dpois
for the Poisson distribution.
dgenpois(x = seq(0,20), lambda1 = 10, lambda2 = 0.5)
pgenpois(q = 5, lambda1 = 10, lambda2 = 0.5)
hist(rgenpois(n = 1000, lambda1 = 10, lambda2 = 0.5) )