dist_degenerate
The degenerate distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_degenerate(x)
Arguments
x |
The value of the distribution. |
Details
The degenerate distribution takes a single value which is certain to be observed. It takes a single parameter, which is the value that is observed by the distribution.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a degenerate random variable with value
x = k_0.
Support: R, the set of all real numbers
Mean: k_0
Variance: 0
Probability density function (p.d.f):
f(x) = 1 for x = k_0
f(x) = 0 for x \neq k_0
Cumulative distribution function (c.d.f):
The cumulative distribution function has the form
F(x) = 0 for x < k_0
F(x) = 1 for x ≥ k_0
Moment generating function (m.g.f):
E(e^(tX)) = e^(k_0 t)
Examples
dist_degenerate(x = 1:5)