DiscreteLaplace (version 1.1.1)

Edlaplace: Moments of the discrete Laplace distribution

Description

The function provides the expected value and the variance of the SDL, and the expectation of its absolute value.

Usage

Edlaplace(p, q)

Arguments

p

the first parameter, in $(0,1)$, of the DSL

q

the second parameter, in $(0,1)$, of the DSL

Value

A list of three items:

E1

expected value

E1a

expectation of the absolute value

V

variance

Details

$E(X;p,q)=\frac{1}{1-p}-\frac{1}{1-q}=\frac{p}{1-p}-\frac{q}{1-q}$,

$E(|X|;p,q)=\frac{q(1-p)^2+p(1-q)^2}{(1-qp)(1-q)(1-p)}$,

$V(X;p,q)=\frac{1}{(1-p)^2(1-q)^2}[\frac{q(1-p)^3(1+q)+p(1-q)^3(1+p)}{1-pq}-(p-q)^2]$

References

T. J. Kozubowski, S. Inusah (2006) A skew Laplace distribution on integers, Annals of the Institute of Statistical Mathematics, 58: 555-571

See Also

ddlaplace

Examples

# ex.1
p<-0.5
q<-0.4
Edlaplace(p, q)
# ex.2
p<-0.1
q<-0.9
Edlaplace(p, q)