dstabledist (version 0.1.0)

pgdstable: 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)

Value

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

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.

References

Steutel_1979dstabledist

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')