| PearsonII {PearsonDS} | 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 a,
location, scale for Pearson type II distribution
(in this order!).
|
log, log.p |
logical; if TRUE, probabilities p are given as log(p).
|
lower.tail |
logical; if TRUE, probabilities are P[X<=x],
otherwise, P[X>x].
|
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)=Gamma(2a)/ (Gamma(a)^2) (((x-lambda)/s)*(1-((x-lambda)/s)))^(a-1)
for a>0, s<>0, 0<(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)