A cumulative distribution function is a nondecreasing function
defined on the interval
- ∞,∞
, with values in
the interval
0, 1
. The definition of a distribution function
generally describes only the values where the function is positive, the
implicit assumption being that the distribution function is zero up to that
point. For discrete cumulative distribution functions, the definition also
gives only the values where the function changes, the implicit assumption
being that the cumulative distribution function is a step function.
Commonly, definitions of these functions are stated only for integers. The
definition of a density
function also generally describes only the values where the function is
positive, the implicit assumption being that the function is zero elsewhere.
These distribution and density functions satisfy the relationships
f (x) | = | ![]() |
|
F(x) | = | ![]() |
Scientific Notebook includes several families of distributions: Normal, Cauchy, Student's t, Chi-square, F, Exponential, Weibull, Gamma, Beta, Uniform, Binomial, Poisson, and Hypergeometric.