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

$$F(x) = 0 for x < k_0$$ $$F(x) = 1 for x \ge k_0$$

Moment generating function (m.g.f):

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

## Examples

dist_degenerate(x = 1:5)
#> <distribution[5]>
#> [1] 1 2 3 4 5