inverseCDF | R Documentation |
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.
inverseCDF(p, CDF, ...)
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 |
... |
named parameters to be passed to the CDF function; see Examples; |
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.
a vector of the same length as p
with the corresponding quantiles.
Mike Meredith
# 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)
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