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.

## 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)
#> <distribution[5]>
#> [1] 1 2 3 4 5
```