ddlaplace {DiscreteLaplace} | R Documentation |
Probability mass function, cumulative distribution function, quantile function and random generation of the DSL
Description
The function computes the probability mass function, the cumulative distribution function, the quantile function of the DSL and implements random generation.
Usage
ddlaplace(x, p, q)
pdlaplace(x, p, q)
qdlaplace(prob, p, q)
rdlaplace(n, p, q)
Arguments
x |
vector of quantiles |
p |
the first parameter |
q |
the second parameter |
prob |
vector of probabilities |
n |
number of observations |
Details
The pmf of the SDL is given by
P(X=x; p, q)=\frac{(1-p)(1-q)}{1-pq}p^x; x=0,1,2,3,\dots
P(X=x; p, q)=\frac{(1-p)(1-q)}{1-pq}q^{|x|}; x=0,-1,-2,-3,\dots
whereas the cumulative distribution function is given by
F(x; p, q)=P(X\leq x)=\frac{(1-p)q^{-\lfloor x\rfloor}}{1-pq},x<0
F(x; p, q)=P(X\leq x)=1-\frac{(1-q)p^{\lfloor x\rfloor+1}}{1-pq},x\geq 0
Value
ddlaplace
returns the probability of x
; pdlaplace
returns the cumulate probability of x
; qdlaplace
returns the prob
- quantile; rdlaplace
returns a random sample of size n
from DSL.
Author(s)
Alessandro Barbiero, Riccardo Inchingolo
References
Tomasz J. Kozubowski, Seidu Inusah (2006) A skew Laplace distribution on integers, Annals of the Institute of Statistical Mathematics, 58: 555-571
See Also
Examples
# pmf
p<-0.7
q<-0.45
x<--10:10
prob<-ddlaplace(x, p, q)
plot(x, prob, type="h")
prob<-ddlaplace(x, q, p) # swap the parameters
plot(x, prob, type="h")
ddlaplace(-4:4, 1:9/10, 9:1/10) # letting p and q be vectors
# cdf
p<-0.2
q<-0.5
x<-c(-3, -1, pi)
pdlaplace(x, p, q)
# quantile function
p<-0.8
q<-0.4
prob<-c(0.2,0.5,0.8)
x<-qdlaplace(prob, p, q)
x # check
upper<-pdlaplace(x, p, q)
upper
lower<-pdlaplace(x-1, p, q)
lower
lower<=prob & prob<=upper
# random generation
n<-100
p<-0.3
q<-0.5
x<-rdlaplace(n, p, q)
x
t<-table(x)
t
plot(t)