Inverse Distribution
Functions
For a distribution function F mapping
- ∞,∞
into
0, 1
, the inverse distribution function G
performs the corresponding inverse mapping from (a subset of)
0, 1
into
- ∞,∞
; that is,
G
F
x
= x and
F
G
α
= α. Equivalently,
Note that the value that is exceeded with probability α is
given by the function
G(1 - α). This function is also of interest.
Prob X≤G 1 - α = F(x) |
= 1 - α = 1 - Prob X≤G α ![$\displaystyle \left.\vphantom{ X\leq G\left( \alpha \right) }\right]$](img24.png) |
In Scientific Notebook, when cumulative distribution functions are
named
FunctionDist, then the inverse cumulative distribution
functions are named
FunctionInv. For example,
NormalInv is the name of the inverse cumulative distribution function for the
normal distribution.