dist_negative_binomial
The Negative Binomial distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_negative_binomial(size, prob)
Arguments
size |
target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer. |
prob |
probability of success in each trial. |
Details
A generalization of the geometric distribution. It is the number
of failures in a sequence of i.i.d. Bernoulli trials before
a specified number of successes (size) occur. The probability of success in
each trial is given by prob.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a Negative Binomial random variable with
success probability prob = p and the number of successes size =
r.
Support: \{0, 1, 2, 3, ...\}
Mean: \frac{p r}{1-p}
Variance: \frac{pr}{(1-p)^2}
Probability mass function (p.m.f):
f(k) = (k+r-1)!/(k!(r-1)!) (1-p)^r p^k
Cumulative distribution function (c.d.f):
Too nasty, omitted.
Moment generating function (m.g.f):
\frac{(1-p)^r}{(1-pe^t)^r}, t < -\log p
See Also
Examples
dist <- dist_negative_binomial(size = 10, prob = 0.5) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7)