PearsonVI | R Documentation |
Density, distribution function, quantile function and random generation for the Pearson type VI (aka Beta prime) distribution.
dpearsonVI(x, a, b, location, scale, params, log = FALSE)
ppearsonVI(q, a, b, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
qpearsonVI(p, a, b, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
rpearsonVI(n, a, b, location, scale, params)
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
a |
first shape parameter of Pearson type VI distribution. |
b |
second shape parameter of Pearson type VI distribution. |
location |
location parameter of Pearson type VI distribution. |
scale |
scale parameter of Pearson type VI distribution. |
params |
vector/list of length 4 containing parameters |
log , log.p |
logical; if |
lower.tail |
logical; if |
Pearson type VI distributions are (location-scale transformations
of) Beta prime distributions, and Beta prime distributions are
scaled F-distributions. The above functions are
thus implemented via calls to df
, pf
,
qf
and rf
(contained in package stats
).
The probability density function with parameters a
, b
,
scale
=s
and location
=\lambda
is given by
f(x)=\frac{\Gamma(a+b)}{|s|\Gamma(a)\Gamma(b)}\left(\frac{x-\lambda}{s}
\right)^{a-1}\left(1+\frac{x-\lambda}{s}\right)^{-a-b}
for a>0
, b>0
, s\ne 0
,
\frac{x-\lambda}{s}>0
.
dpearsonVI
gives the density, ppearsonVI
gives the
distribution function, qpearsonVI
gives the quantile function,
and rpearsonVI
generates random deviates.
Negative values for scale
are permitted to allow for negative skewness.
Martin Becker martin.becker@mx.uni-saarland.de
See the references in FDist
.
FDist
,
PearsonDS-package
,
Pearson
## define Pearson type VI parameter set with a=2, b=3, location=1, scale=2
pVIpars <- list(a=2, b=3, location=1, scale=2)
## calculate probability density function
dpearsonVI(seq(1,6,by=1),params=pVIpars)
## calculate cumulative distribution function
ppearsonVI(seq(1,6,by=1),params=pVIpars)
## calculate quantile function
qpearsonVI(seq(0.1,0.9,by=0.2),params=pVIpars)
## generate random numbers
rpearsonVI(5,params=pVIpars)
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