PearsonVII | R Documentation |
Density, distribution function, quantile function and random generation for the Pearson type VII (aka Student's t) distribution.
dpearsonVII(x, df, location, scale, params, log = FALSE)
ppearsonVII(q, df, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
qpearsonVII(p, df, location, scale, params, lower.tail = TRUE,
log.p = FALSE)
rpearsonVII(n, df, location, scale, params)
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
df |
degrees of freedom of Pearson type VII distribution |
location |
location parameter of Pearson type VII distribution. |
scale |
scale parameter of Pearson type VII distribution. |
params |
vector/list of length 3 containing parameters |
log , log.p |
logical; if |
lower.tail |
logical; if |
The Pearson type VII distribution is a simple (location-scale) transformation
of the well-known Student's t distribution; the probability density function
with parameters df
=n
, location
=\lambda
and
scale
=s
is given by
f(x) = \frac{1}{|s|}\frac{\Gamma(\frac{n+1}{2})}{\sqrt{n \pi} \Gamma(\frac{n}{2})}
\left(1 + \frac{(\frac{x-\lambda}{s})^2}{n}\right)^{-\frac{n+1}{2}}
for s\ne 0
.
The above functions are thus only wrappers for dt
,
pt
, qt
and rt
contained in package
stats
.
dpearsonVII
gives the density, ppearsonVII
gives the
distribution function, qpearsonVII
gives the quantile function,
and rpearsonVII
generates random deviates.
Martin Becker martin.becker@mx.uni-saarland.de
See the references in TDist
.
TDist
,
PearsonDS-package
,
Pearson
## define Pearson type VII parameter set with df=7, location=1, scale=1
pVIIpars <- list(df=7, location=1, scale=1)
## calculate probability density function
dpearsonVII(-2:4,params=pVIIpars)
## calculate cumulative distribution function
ppearsonVII(-2:4,params=pVIIpars)
## calculate quantile function
qpearsonVII(seq(0.1,0.9,by=0.2),params=pVIIpars)
## generate random numbers
rpearsonVII(5,params=pVIIpars)
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