CornishFisher: Functions for Cornish-Fisher density, CDF, random number...

In R-Finance/FactorAnalytics: factor analysis

Description

• rCornishFisher simulate observations based on Cornish-Fisher quantile expansion given mean, standard deviation, skewness and excess kurtosis.

• dCornishFisher Computes Cornish-Fisher density from two term Edgeworth expansion given mean, standard deviation, skewness and excess kurtosis.

• pCornishFisher Computes Cornish-Fisher CDF from two term Edgeworth expansion given mean, standard deviation, skewness and excess kurtosis.

• qCornishFisher Computes Cornish-Fisher quantiles from two term Edgeworth expansion given mean, standard deviation, skewness and excess kurtosis.

Usage

  dCornishFisher(x, n, skew, ekurt)

  pCornishFisher(q, n, skew, ekurt)

  qCornishFisher(p, n, skew, ekurt)

  rCornishFisher(n, sigma, skew, ekurt, seed = NULL)

Arguments

n	Scalar, number of simulated values in rCornishFisher. Sample length in density,distribution,quantile function.
sigma	Scalar, standard deviation.
skew	Scalar, skewness.
ekurt	Scalar, excess kurtosis.
seed	Set seed here. Default is NULL.
x,q	Vector of standardized quantiles. See detail.
p	Vector of probabilities.

Details

CDF(q) = Pr(sqrt(n)*(x_bar-mu)/sigma < q)

Value

n Simulated values from Cornish-Fisher distribution.

Author(s)

Eric Zivot and Yi-An Chen.

References

1. A.DasGupta, "Asymptotic Theory of Statistics and Probability", Springer Science+Business Media,LLC 2008

2. Thomas A.Severini, "Likelihood Methods in Statistics", Oxford University Press, 2000

Examples

## Not run: 
 # generate 1000 observation from Cornish-Fisher distribution
rc <- rCornishFisher(1000,1,0,5)
hist(rc,breaks=100,freq=FALSE,main="simulation of Cornish Fisher Distribution",
    xlim=c(-10,10))
lines(seq(-10,10,0.1),dnorm(seq(-10,10,0.1),mean=0,sd=1),col=2)
# compare with standard normal curve

# example from A.dasGupta p.188 exponential example
# x is iid exp(1) distribution, sample size = 5
# then x_bar is Gamma(shape=5,scale=1/5) distribution
q <- c(0,0.4,1,2)
# exact cdf
pgamma(q/sqrt(5)+1,shape=5,scale=1/5)
# use CLT
pnorm(q)
# use edgeworth expansion
pCornishFisher(q,n=5,skew=2,ekurt=6)

## End(Not run)

R-Finance/FactorAnalytics documentation built on May 8, 2019, 3:51 a.m.