PearsonVII {PearsonDS} | 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) = Gamma((n+1)/2) / (sqrt(n pi) Gamma(n/2)) (1 + ((x-lambda)/s)^2/n)^-((n+1)/2)
for s<>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)