pgdstable {dstabledist}

The discrete stable distribution: probability generating function

Description

Computes probability generating function of a discrete stable distribution DS(alpha,lambda).

Usage

pgdstable(z, alpha, lambda = 1)

Arguments

z

argument of probability generating function, z in the interval= [-1, 1].

alpha

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

lambda

positive location parameter lambda>0.

Value

Returns value of probability generating function of DS(alpha,lambda). A warning is displayed for invalid parameter values.

References

Steutel FW, van Harn K (1979). “Discrete Analogues of Self-Decomposability and Stability.” The Annals of Probability, 7(5), 893 – 899. doi:10.1214/aop/1176994950.

Examples

pgdstable(c(-1,0,1),0.5,1)
pgdstable(c(-1,0,1),1,1) #This is Poisson
 curve(pgdstable(x,1,lambda=1), c(-1,1),col=1,ylab='prob. gen. fun.',xlab='z')
 curve(pgdstable(x,0.5,lambda=1), c(-1,1),col=2,add=TRUE)
 curve(pgdstable(x,0.2,lambda=1), c(-1,1),col=4,add=TRUE)
legend('topleft',legend=c(1,0.5,0.1), col=c(1,2,4), lty = 1, title='alpha')