CUMULATIVE DISTRIBUTION AND QNTILE FUNCTIONS OF A GPD OBJECT

Description

Cumulative distribution function and quantiles for the distribution of a GPD object (as produced for example by the semi-parametric estimation procedure gpd.tail).

Usage

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         gpd.1p(x, est.object, linear = TRUE) 
         gpd.1q(p, est.object, linear = TRUE) 
         gpd.2p(x, est.object, linear = TRUE) 
         gpd.2q(p, est.object, linear = TRUE) 

Arguments

x

A numeric vector of values at which the cdf is computed

p

A numeric vector of probabilities at which the quantiles are computed

est.object

An object of class gpd as the output of gpd.tail.

OPTIONAL ARGUMENTS
linear

A boolean. If TRUE (default), the empirical cdf and quantile function are linearly interpolated for lower < x < upper. If FALSE, the empirical cdf and quantile function are returned for lower < x < upper.

Value

Functions gpd.1p and gpd.2p return a vector of the same length as x comprising the values of the cumulative distribution function of the distribution determined by est.obj computed at the points x.

Functions gpd.1q and gpd.2q return a vector of the same length as q comprising the values of the quantiles of the distribution determined by est.obj computed at the points q.

Author(s)

Rene Carmona, rcarmona@princeton.edu

See Also

pgpd, qgpd

Examples

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# One tail
data("BCofLRet")
NZ <- (BCofLRet !=0)
BLRet <- BCofLRet[NZ]
X <- BLRet[BLRet > 0]
x.est <- gpd.tail(X)

y <- c(10:500)/1000
plot(y, gpd.1p(y,x.est), log = "x", type = "l")
big.X <- sort(X) > 0.01
points((sort(X))[big.X], (ppoints(sort(X)))[big.X])

# random generation from this distribution:
data("BCofLRet")
NZ <- (BCofLRet !=0)
BLRet <- BCofLRet[NZ]
X <- BLRet[BLRet != 0]
x.est <- gpd.tail(X, upper = 0.015, lower = -0.015, method = "lmom")
n <- length(X)
Y <- gpd.2q(runif(n), x.est)
plot(X, ylim = c(-0.3,0.3))
plot(Y, col = 4, , ylim = c(-0.3,0.3))