dnormp | R Documentation |
Density function for the exponential power distribution with location parameter mu
,
scale parameter sigmap
and shape parameter p
.
dnormp(x, mu=0, sigmap=1, p=2, log=FALSE)
x |
Vector of quantiles. |
mu |
Vector of location parameters. |
sigmap |
Vector of scale parameters. |
p |
Shape parameter. |
log |
Logical; if TRUE, the density is given as log(density). |
If mu
, sigmap
or p
are not specified they assume the default values 0, 1 and 2,
respectively.
The exponential power distribution has density function
f(x) = \frac{1}{2 p^{(1/p)} \Gamma(1+1/p) \sigma_p} e^{-\frac{|x - \mu|^p}{p \sigma_p^p}}
where \mu
is the location parameter, \sigma_p
the scale parameter and p
the
shape parameter.
When p=2
the exponential power distribution becomes the Normal Distribution, when
p=1
the exponential power distribution becomes the Laplace Distribution, when
p\rightarrow\infty
the exponential power distribution becomes the Uniform Distribution.
dnormp
gives the density function of an exponential power distribution.
Angelo M. Mineo
Normal
for the Normal distribution, Uniform
for the Uniform distribution,
and Special
for the Gamma function.
## Compute the density for a vector x with mu=0, sigmap=1 and p=1.5
## At the end we have the graph of the exponential power distribution
## density function with p=1.5
x <- c(-1, 1)
f <- dnormp(x, p=1.5)
print(f)
plot(function(x) dnormp(x, p=1.5) , -4, 4,
main = "Exponential power distribution density function (p=1.5)", ylab="f(x)")
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