dist_degenerate {distributional}

The degenerate distribution

Description

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.

Usage

dist_degenerate(x)

Arguments

x

The value of the distribution.

Details

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 \ge k_0

Moment generating function (m.g.f):

E(e^{tX}) = e^{k_0 t}

Examples

dist_degenerate(x = 1:5)