gives the inverse of the cumulative distribution function for the distribution dist as a function of the variable q.
- The inverse CDF at q is also referred to as the q quantile of a distribution.
- For a continuous distribution dist the inverse CDF at q is the value x such that CDF[dist,x]q.
- For a discrete distribution dist the inverse CDF at q is the smallest integer x such that CDF[dist,x]≥q.
- The value q can be symbolic or any number between 0 and 1.
Examplesopen allclose all
Basic Examples (2)
Parametric Distributions (5)
Derived Distributions (3)
InverseCDF for a truncated distribution:
Nonparametric Distributions (2)
Generalizations & Extensions (2)
InverseCDF threads element-wise over lists:
Properties & Relations (7)
InverseCDF[,p] is continuous and strictly increasing for 0≤p≤1 and continuous:
InverseCDF[,p] is piecewise constant and increasing for 0≤p≤1 and discrete:
InverseCDF[,p] is left-continuous and increasing for 0≤p≤1 and mixed:
CDF[,InverseCDF[,p]]p for a continuous distribution :
CDF[,InverseCDF[,p]]≥p for a discrete distribution :