Approximate quantile via Cornish-Fisher expansion.
Approximate the quantile function of a distribution via its cumulants.
qapx_cf(p, raw.cumulants, support=c(-Inf,Inf), lower.tail = TRUE, log.p = FALSE)
p: where to evaluate the approximate distribution.raw.cumulants: an atomic array of the 1st through kth raw cumulants. The first value is the mean of the distribution, the second should be the variance of the distribution, the remainder are raw cumulants.support: the support of the density function. It is assumed that the density is zero on the complement of this open interval. This defaults to c(-Inf,Inf) for the normal basis, c(0,Inf) for the gamma basis, and c(0,1) for the Beta, and c(-1,1) for the arcsine and wigner.lower.tail: whether to compute the lower tail. If false, we approximate the survival function.log.p: logical; if TRUE, probabilities p are given as .The approximate quantile at p.
Given the cumulants of a probability distribution, we approximate the quantile function via a Cornish-Fisher expansion.
Monotonicity of the quantile function is not guaranteed.
# normal distribution: pvals <- seq(0.001,0.999,length.out=501) q1 <- qapx_cf(pvals, c(0,1,0,0,0,0,0)) q2 <- qnorm(pvals) q1 - q2
Steven E. Pav shabbychef@gmail.com
Lee, Y-S., and Lin, T-K. "Algorithm AS269: High Order Cornish Fisher Expansion." Appl. Stat. 41, no. 1 (1992): 233-240. http://www.jstor.org/stable/2347649
Lee, Y-S., and Lin, T-K. "Correction to Algorithm AS269: High Order Cornish Fisher Expansion." Appl. Stat. 42, no. 1 (1993): 268-269. http://www.jstor.org/stable/2347433
AS 269. http://lib.stat.cmu.edu/apstat/269
Jaschke, Stefan R. "The Cornish-Fisher-expansion in the context of Delta-Gamma-normal approximations." No. 2001, 54. Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2001. http://www.jaschke-net.de/papers/CoFi.pdf
dapx_gca, papx_gca, AS269, rapx_cf