PearsonII | R Documentation |
Density, distribution function, quantile function and random generation for the Pearson type II (aka symmetric Beta) distribution.
dpearsonII(x, a, location, scale, params, log = FALSE)
ppearsonII(q, a, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
qpearsonII(p, a, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
rpearsonII(n, a, location, scale, params)
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
a |
shape parameter of Pearson type II distribution. |
location |
location parameter of Pearson type II distribution. |
scale |
scale parameter of Pearson type II distribution. |
params |
vector/list of length 3 containing parameters |
log , log.p |
logical; if |
lower.tail |
logical; if |
Essentially, Pearson type II distributions are (location-scale transformations
of) symmetric Beta distributions, the above
functions are thus simple wrappers for dbeta
, pbeta
,
qbeta
and rbeta
contained in package stats
.
The probability density function with parameters a
,
scale
=s
and location
=\lambda
is given by
f(x)=\frac{1}{|s|}\frac{\Gamma(2a)}{\Gamma(a)^2}\left(\frac{x-\lambda}{s}\cdot
\left(1-\frac{x-\lambda}{s}\right)\right)^{a-1}
for a>0
, s\ne 0
,
0<\frac{x-\lambda}{s}<1
.
dpearsonII
gives the density, ppearsonII
gives the
distribution function, qpearsonII
gives the quantile function,
and rpearsonII
generates random deviates.
Martin Becker martin.becker@mx.uni-saarland.de
See the references in Beta
.
Beta
,
PearsonDS-package
,
Pearson
## define Pearson type II parameter set with a=2, location=1, scale=2
pIIpars <- list(a=2, location=1, scale=2)
## calculate probability density function
dpearsonII(seq(1,3,by=0.5),params=pIIpars)
## calculate cumulative distribution function
ppearsonII(seq(1,3,by=0.5),params=pIIpars)
## calculate quantile function
qpearsonII(seq(0.1,0.9,by=0.2),params=pIIpars)
## generate random numbers
rpearsonII(5,params=pIIpars)
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