View source: R/dist_degenerate.R
dist_degenerate | R Documentation |
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.
dist_degenerate(x)
x |
The value of 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}
dist_degenerate(x = 1:5)
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