In this article, you will understand what cumulative distribution function is, its properties, formulas, applications and examples. A number of results exist to quantify the rate of convergence of the empirical distribution function to the underlying cumulative distribution functioncitation needed.
Creative Commons Attribution NonCommercial License 4. Furthermore,
Every function with these four properties is a CDF, i. 4)Interpreting the
N
{\displaystyle N}
random variables as a random vector
X
see here =
(
X
1
,
,
X
N
)
T
{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{N})^{T}}
yields a shorter notation:
Every multivariate CDF is:
Any function satisfying the above four properties is not a multivariate CDF, unlike in the single dimension case.
3 Shocking To Simulation
If the CDF F is strictly increasing and continuous then
F
1
(
p
)
,
p
[
0
,
1
]
,
{\displaystyle F^{-1}(p),p\in [0,1],}
is the unique real number
{\displaystyle x}
such that
F
(
x
)
=
p
{\displaystyle F(x)=p}
. .