HDInterval (version 0.2.4)

inverseCDF: Inverse Cumulative Density Function

Description

Given a cumulative density function, calculates the quantiles coresponding to given probabilities, ie, "converts" a CDF to an ICDF. The function method for hdi requires an ICDF, which is not always available for custom distributions.

Usage

inverseCDF(p, CDF, ...)

Value

a vector of the same length as p with the corresponding quantiles.

Arguments

p

a vector of probabilities. Values less than 1e6 will be replaced with 1e6 and values greater than (1 - 1e-6) will be replaced with (1 - 1e-6), without a warning.

CDF

a cumulative density function; standard CDFs in R begin with p-, eg, pnorm.

...

named parameters to be passed to the CDF function; see Examples; log.p and lower.tail are not supported and generate an error.

Author

Mike Meredith

Details

The function uses a search algorithm to find the value of q which corresponds to p. This suffers from imprecision, especially for sections of the CDF which are relatively flat, as is usually the case close to p = 0 or 1.

Examples

# Try with pgamma/qgamma
inverseCDF(c(0.025, 0.975), pgamma, shape=2.5, rate=2) # 95% interval
qgamma(c(0.025, 0.975), shape=2.5, rate=2) # for comparison
inverseCDF(c(0, 1), pgamma, shape=2.5, rate=2) # nonsense, fixed internally...
inverseCDF(c(1e-6, 1 - 1e-6), pgamma, shape=2.5, rate=2) # ...same.

# Plug inverseCDF into hdi, need to specify the CDF
hdi(inverseCDF, CDF=pgamma, shape=2.5, rate=2)
hdi(qgamma, shape=2.5, rate=2) # for comparison

# for a custom density, here a mixture of normals
# the PDF
dmixg <- function(x)
  0.6 * dnorm(x, 0, 1) + 0.4 * dnorm(x, 4, 2^0.5)
curve(dmixg, -5, 10)
# and the CDF
pmixg <- function(q)
  0.6 * pnorm(q, 0, 1) + 0.4 * pnorm(q, 4, 2^0.5)
curve(pmixg, -5, 10)
# Now plug into inverseCDF and hdi
inverseCDF(c(0.025, 0.975), pmixg)
hdi(inverseCDF, CDF=pmixg)