ddstable {dstabledist}

The discrete stable distribution: formulae for the probabilities (density)

Description

Computes the value of the formulae for the probabilities (density) of a discrete stable distribution DS(alpha,lambda), by combining the explicit and fast asymptotic formulae.

Usage

ddstable(x, alpha, lambda)

Arguments

x

a vector of non-negative integer quantiles, k>=0

alpha

tail index parameter alpha in the interval= (0, 1]

lambda

positive location parameter lambda>0

Value

Returns the value of the formulae for the probabilities (density) of DS(alpha,lambda).

References

Christoph G, Schreiber K (1998). “Discrete stable random variables.” Statistics & Probability Letters, 37(3), 243-247. ISSN 0167-7152, doi:10.1016/S0167-7152(97)00123-5.

Examples

ddstable(c(0,1,2,100),1,lambda=1)#This is Poisson with lambda=1
dpois(c(0,1,2,100),1)#Checking with dpois
ddstable(c(0,1,2,100),0.5,lambda=1) # tail is heavier
ddstable(c(0,1,2,3,6,100),0.5,lambda=3) # change in location