| Type: | Package |
| Title: | The Discrete Stable Distribution Functions |
| Version: | 0.1.0 |
| Maintainer: | Krutto Annika <annikakrutto@gmail.com> |
| Description: | Probability generating function, formulae for the probabilities (discrete density) and random generation for discrete stable random variables. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| Imports: | stabledist, stats, Rdpack |
| RdMacros: | Rdpack |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-05-02 19:57:13 UTC; annikakrutto |
| Author: | Krutto Annika 
[aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2023-05-03 18:50:05 UTC |
dstabledist: The Discrete Stable Distribution Functions
Description
Probability generating function, formulae for the probabilities (discrete density) and random generation for discrete stable random variables.
Author(s)
Maintainer: Krutto Annika annikakrutto@gmail.com (ORCID)
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, |
alpha |
tail index parameter |
lambda |
positive location parameter |
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
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, |
alpha |
tail index parameter |
lambda |
positive location parameter |
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')
The discrete stable distribution: random generation
Description
Generates random variates from a discrete stable distribution DS(alpha,lambda).
Usage
rdstable(n, alpha, lambda = 1)
Arguments
n |
number of random values to return. |
alpha |
tail index parameter |
lambda |
positive location parameter |
Value
returns random variates from DS(alpha,lambda). A warning is displayed for invalid parameter values.
References
Devroye L (1993). “A triptych of discrete distributions related to the stable law.” Statistics & Probability Letters, 18(5), 349-351. ISSN 0167-7152, doi:10.1016/0167-7152(93)90027-G.
Examples
rdstable(10,alpha=1,lambda=1) #this is Poisson
rdstable(10,alpha=0.5,lambda=1) # heavier tail more prone to extremes
rdstable(10,alpha=0.1,lambda=1) # heavier tail more prone to extremes