pcf.func: Calculates a piecewise constant function for some illustrative purposes

Description

Calculates a piecewise constant function of a given functional form: Gaussian or a mixture of Gaussians, or functions with a given copula, ...

Usage

pcf.func(func, N, 
sig = rep(1, length(N)), support = NULL, theta = NULL, 
g=1, M = NULL, p = NULL, mul = 3, t = NULL, 
marginal = "normal", r = 0, 
mu = NULL, xi = NULL, Omega = NULL, alpha = NULL, df = NULL,
a = 0.5, b = 0.5, distr = FALSE, std = 1, lowest = 0)

Arguments

func

a character string; the possibilities are "mixt", "normal","student","gumbel","frank","clayton", "skewgauss", "prod", "epan", "hat"

vector of d positive integers; the dimension of the grid where the function will be evaluated; we evaluate the function on a regular grid which contains the support of the function

sig

mixnum*d matrix of positive real numbers; the standard deviations of the marginals in a mixture of Gaussians, or the scaling factors of the student and uniform copulas

support

2*d vector of reals gives the d intervals of a rectangular support

theta

rotation angle

parameter of the Archimedean copulas

mixnum*d matrix of positive real numbers; the means of the components in a mixture of Gaussians

mixnum-vector of probabilities; mixture weights

mul

internal parameter

parameter of the Student marginals (degrees of freedom)

marginal

marginal distributions for the copulas; "normal", "student", or "unif"

parameter

Omega

parameter

alpha

skeweness parameter for the skewed Gaussian density

degrees of freedom for the Student copula

a, b

parameters of the hat function

distr

TRUE if the distribution function is to be drawn instead of the density

std

standard deviation in the 1D case

lowest

real value; for densities equal to 0, otherwise is equal to the minimum of the function

Value

a piecewise constant function object, see the web page

References

http://www.rni.helsinki.fi/~jsk/denpro/

Examples

Run this code

# Elliptical copulas

N<-c(32,32)  # choose the grid size
copula<-c("gauss","student")
margin<-c("normal","student","unif")
b<-4
support<-c(-b,b,-b,b)

ci<-1        # copula, ci = 1, 2
r<-0.5       # parameter of the copula
df<-2        # degrees of freedom for the Student copula 

mi<-1        # margin, mi = 1, 2, 3
sig<-c(1,1)  # std:s for the margins
t<-c(2,2)    # degreeds of freedom for the student margin

ef<-pcf.func(copula[ci],N,marginal=margin[mi],support=support,
             r=r,df=df,sig=sig,t=t)

dp<-draw.pcf(ef)
contour(dp$x,dp$y,dp$z)   

persp(dp$x,dp$y,dp$z,theta=30,phi=30)   

# Archimedean copulas

N<-c(32,32)  # choose the grid size
copula<-c("gumbel","frank","clayton")
margin<-c("normal","student","unif")
b<-4
support<-c(-b,b,-b,b)

ci<-1        # copula, ci = 1, 2, 3
g<-2         # parameter of the copula

mi<-1        # margin, mi = 1, 2, 3
sig<-c(1,1)  # std:s for the margins
t<-c(2,2)    # degreeds of freedom for the student margin

ef<-pcf.func(copula[ci],N,marginal=margin[mi],support=support,
             g=g,sig=sig,t=t)

dp<-draw.pcf(ef)
contour(dp$x,dp$y,dp$z)   

persp(dp$x,dp$y,dp$z,theta=30,phi=30)   

# mixture of Gaussians

d<-2
mixnum<-3               #we simulate a mixture of three Gaussians
M<-matrix(0,mixnum,d)   #rows of M contain the means of members of the mixture
M[1,]<-c(0,0)   
M[2,]<-c(4,0)  
M[3,]<-c(0,4)   
sig<-matrix(1,mixnum,d) #rows of sig contain the std:s ot the marginals
p0<-1/mixnum
p<-p0*rep(1,mixnum)     #p is a vector of weights for the mixture members
N<-c(50,50)

pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) 

dp<-draw.pcf(pcf,pnum=c(30,30))
contour(dp$x,dp$y,dp$z,drawlabels=FALSE)
persp(dp$x,dp$y,dp$z)

# skewed Gaussian

func<-"skewgauss"
N<-c(50,50)
support<-c(-6,2,-6,2)
mu<-c(0,0)
sig<-c(3,1)
alpha<-c(6,0)
theta<--3*pi/4

pcf<-pcf.func(func,N,support=support,mu=mu,sig=sig,
               alpha=alpha,theta=theta)

dp<-draw.pcf(pcf,pnum=c(60,60))

contour(dp$x,dp$y,dp$z)

persp(dp$x,dp$y,dp$z,theta=30,phi=30)   

# product of univariate Student densities

func<-"prod"
marginal<-"student"
b<-5; support<-c(-b,b,-b,b)
N<-c(32,32)                 # choose the grid size
t<-0.5                      # degrees of freedom                 
ef<-pcf.func(func,N,t=t,support=support,marginal=marginal)

dp<-draw.pcf(ef)
contour(dp$x,dp$y,dp$z)   

persp(dp$x,dp$y,dp$z,theta=30,phi=30) 

# Bartlett-Epanechnikov

func<-"epan"
N<-c(50,50)
sig<-c(1,1)

ef<-pcf.func(func,N,sig)

dp<-draw.pcf(ef)
contour(dp$x,dp$y,dp$z)

persp(dp$x,dp$y,dp$z,theta=30,phi=30)