claytonmix {QRMlib}R Documentation

Mixing Distribution on Unit Interval Yielding Clayton Copula Model

Description

density, cumulative probability, and random generation for a mixture distribution on the unit interval which gives an exchangeable Bernoulli mixture model equivalent to a Clayton copula model

Usage

dclaytonmix(x, pi, theta) 
pclaytonmix(q, pi, theta) 
rclaytonmix(n, pi, theta)

Arguments

x values at which density should be evaluated
q values at which cumulative distribution should be evaluated
n sample size
pi parameter of distribution
theta parameter of distribution

Details

see page 362 in QRM

Value

values of density (dclaytonmix), distribution function (pclaytonmix) or random sample (rclaytonmix)

Author(s)

documentation by Scott Ulman for R-language distribution

See Also

dbeta, dprobitnorm

Examples

#probability of only one obligor defaulting B class (see Table 8.6 in QRM book)
pi.B <- 0.0489603; 
#joint probability of two obligors defaulting B class (see Table 8.6 in QRM book)
pi2.B <- 0.003126529; 
# Calibrate Calyton copula model to pi.B and pi2.B
claytonmix.pars <- cal.claytonmix(pi.B,pi2.B)
# We could also look at mixing densities. Get probability of Clayton mix
# This picture essentially shows large sample asymptotics
#Build 1000 equally-spaced values on unit interval (multiples of .000999); 
#discard all values except those below 0.25
q <- (1:1000)/1001;
q <- q[q<0.25]; #reduce to lowest 250 values
#get probabilities for each of 250 lowest values on unit interval
d.claytonmix <- dclaytonmix(q,claytonmix.pars[1],claytonmix.pars[2]);

[Package QRMlib version 1.4.4 Index]