pnormp {normalp} | R Documentation |
Probability function for the normal of order p distribution with location parameter
mu
, scale parameter sigmap
and structure parameter p
.
pnormp(q, mu=0, sigmap=1, p=2, lower.tail=TRUE, log.pr=FALSE)
q |
Vector of quantiles. |
mu |
Vector of location parameters. |
sigmap |
Vector of scale parameters. |
p |
Structure parameter. |
lower.tail |
Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X>x]. |
log.pr |
Logical; if TRUE, probabilities pr are given as log(pr). |
If mu
, sigmap
or p
are not specified they assume the default values 0, 1 and 2,
respectively.
The normal of order p distribution has density function
f(x) = 1/(2 p^(1/p) Gamma(1+1/p) sigmap) exp{-|x - mu|^p/(p sigmap^p)}
where mu is the location parameter, sigmap the scale parameter and p the structure parameter. When p=2 the Normal of Order p Distribution becomes the Normal (Gaussian) Distribution, when p=1 the Normal of Order p Distribution becomes the Laplace Distribution, when p->infinity the Normal of Order p Distribution becomes the Uniform Distribution.
pnormp
gives the probability of a normal of order p distribution.
Angelo M. Mineo
Normal
for the Normal distribution, Uniform
for the Uniform distribution, and Special
for the Gamma function.
## Compute the distribution function for a vector x with mu=0, sigmap=1 and p=1.5 ## At the end we have the graph of the Normal of order 1.5 distribution function. x <- c(-1, 1) pr <- pnormp(x, p=1.5) print(pr) plot(function(x) pnormp(x, p=1.5), -4, 4, main = "Normal of order p Distribution Function (p=1.5)", ylab="F(x)")