BivariateTools {fMultivar} | R Documentation |
A collection and description of functions
for managing bivariate data sets. The functions
include a grid generator, a kernel density
estimator, a histogram counter, and a suite of
bivariate elliptical distribution functions.
The functions are:
grid2d | Creates from two vectors x-y grid coordinates, |
density2d | returns 2D Kernel Density Estimates, |
hist2d | returns 2D Histogram Counts, |
integrate2d | integrates over a two dimensional unit square, |
pnorm2d | computes bivariate normal distribution function, |
dnorm2d | computes bivariate normal density function, |
rnorm2d | generates bivariate normal random deviates, |
pcauchy2d | computes bivariate Cauchy distribution function, |
dcauchy2d | computes bivariate Cauchy density function, |
rcauchy2d | generates bivariate Cauchy random deviates, |
pt2d | computes bivariate Student-t distribution function, |
dt2d | computes bivariate Student-t density function, |
rt2d | generates bivariate Student-t random deviates, |
delliptical2d | computes bivariate density for elliptical distributions. |
grid2d(x = (0:10)/10, y = x) density2d(x, y = NULL, n = 20, h = NULL, limits = c(range(x), range(y))) hist2d(x, y = NULL, n = c(20, 20)) integrate2d(fun, error = 1.0e-5, ...) pnorm2d(x, y = x, rho = 0) dnorm2d(x, y = x, rho = 0) rnorm2d(n, rho = 0) pcauchy2d(x, y = x, rho = 0) dcauchy2d(x, y = x, rho = 0) rcauchy2d(n, rho = 0) pt2d(x, y = x, rho = 0, nu = 4) dt2d(x, y = x, rho = 0, nu = 4) rt2d(n, rho = 0, nu = 4) delliptical2d(x, y = x, rho = 0, param = NULL, type = c("norm", "cauchy", "t", "logistic", "laplace", "kotz", "epower"), output = c("vector", "list"))
error |
[integrate2d] - the error bound to be achieved by the integration formula. A numeric value. |
fun |
[integrate2d] - the function to be integrated. The first argument requests the x values, the second the y values, and the remaining are reserved for additional parameters. The integration is over the unit square "[0,1]^2". |
h |
[density2d] - a vector of bandwidths for x and y directions.
Defaults to normal reference bandwidth.
|
limits |
[hist2d] - the limits of the rectangle covered by the grid. |
n |
[density2d] - n - an integer specifying the number of grid points in each direction. The default value is 20. [hist2D] - In this case n may be a scalar or a two element vector.
The default value is 20.[rnorm2d] - the number of random deviates to be generated, an integer value. |
nu |
[*t2d] - the number of degrees of freedom, a numeric value ranging between two and infinity, by default four. |
output |
[*elliptical2d] - output - a character string specifying how the output should be formatted. By default a vector of the same length as u
and v . If specified as "list" then u and
v are expected to span a two-dimensional grid as outputted
by the function grid2d and the function returns a list with
elements $x , y , and z which can be directly
used for example by 2D plotting functions.
|
param |
[delliptical2d] - additional parameters to specify the bivariate density function. Only effective for the Kotz and Exponential Power distribution. For the Kotz distribution we can specify a numeric value, by default defined as param=c(r=sqrt(2)) , and for the Exponential
Power distribution a numeric vector, by default defined as
param=c(r=sqrt(2)),s=1/2 .
|
rho |
[*norm2d][*cauchy2d][*t2d][*elliptical2d] - the correlation parameter, a numeric value ranging between minus one and one, by default zero. |
type |
[*elliptical2d] - the type of the elliptical copula. A character string selected from: "norm" , "cauchy" , "t" , "laplace" ,
"kotz" , or "epower" .
|
x, y |
[grid2d][*norm2d][*t2d] - two numeric vectors defining the x and y coordinates. [density2D][hist2D] - two vectors of coordinates of data. If y is NULL then
x is assumed to be a two column matrix, where the first
column contains the x data, and the second column the
y data.
|
... |
[integrate2d] - parameters passed to the function to be integrated. |
grid2d
returns a list with two vectors named $x
and $y
spanning
the grid defined by the coordinate vectors x
and y
.
density2d
hist2d
returns a list with three elements $x
, $y
, and
$z
. x
and y
are vectors spanning the two
dimensional grid and z
the corresponding matrix. The
output can directly serve as input to the plotting functions
image
, contour
and persp
.
integrate2d
returns a list with the $value
of the integral over the
unit square [0,1]^2, an $error
estimate and the number
of grid $points
used by the integration function.
pnorm2d
returns a vector of probabilities for the normal distribution
function.
pnorm2d
returns a two column matrix of random deviates generated from
the bivariate normal distribution function.
W.N. Venables and B.D. Ripley for the underlying kde2d function,
Adelchi Azzalini for the underlying pnorm2d function,
Gregory R. Warnes for the underlying hist2d function,
Diethelm Wuertz for the Rmetrics R-port.
Azzalini A., (2004); The sn Package; R Reference Guide available from www.r-project.org.
Venables W.N., Ripley B.D., (2002); Modern Applied Statistics with S, Fourth Edition, Springer.
Warnes G.R., (2004); The gregmisc Package; R Reference Guide available from www.r-project.org.
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