PearsonV {PearsonDS} | R Documentation |
Density, distribution function, quantile function and random generation for the Pearson type V (aka Inverse Gamma) distribution.
dpearsonV(x, shape, location, scale, params, log = FALSE) ppearsonV(q, shape, location, scale, params, lower.tail = TRUE, log.p = FALSE) qpearsonV(p, shape, location, scale, params, lower.tail = TRUE, log.p = FALSE) rpearsonV(n, shape, location, scale, params)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
shape |
shape parameter of Pearson type V distribution. |
location |
location parameter of Pearson type V distribution. |
scale |
scale parameter of Pearson type V distribution. |
params |
vector/list of length 3 containing parameters shape ,
location , scale for Pearson type V 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].
|
The Pearson type V distributions are essentially Inverse Gamma distributions.
Thus, all functions are implemented via calls to the corresponding functions
for Gamma distributions, ie. dgamma
, pgamma
, qgamma
and rgamma
in package stats
.
Negative scale
parameters
(which reflect the distribution at location
) are
permitted to allow for negative skewness.
The probability density function with parameters shape
=a,
scale
=s and location
=lambda
is given by
f(x)= 1/(|s|^a Gamma(a)) |x-lambda|^(-a-1) e^-(s/(x-lambda))
for s<>0, a>0 and s/(x-lambda)>0.
dpearsonV
gives the density, ppearsonV
gives the
distribution function, qpearsonV
gives the quantile function,
and rpearsonV
generates random deviates.
The parameter scale
corresponds to the reciprocal value of the
usual scale parameter of the Inverse Gamma distribution.
Martin Becker martin.becker@mx.uni-saarland.de
See the references in GammaDist
.
GammaDist
,
PearsonDS-package
,
Pearson
## define Pearson type V parameter set with shape=3, location=1, scale=-2 pVpars <- list(shape=3, location=1, scale=-0.5) ## calculate probability density function dpearsonV(-4:1,params=pVpars) ## calculate cumulative distribution function ppearsonV(-4:1,params=pVpars) ## calculate quantile function qpearsonV(seq(0.1,0.9,by=0.2),params=pVpars) ## generate random numbers rpearsonV(5,params=pVpars)