dist_negative_binomial {distributional} | R Documentation |
The Negative Binomial distribution
Description
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
.
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
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let be a Negative Binomial random variable with
success probability
prob
= and the number of successes
size
=
.
Support:
Mean:
Variance:
Probability mass function (p.m.f):
Cumulative distribution function (c.d.f):
Too nasty, omitted.
Moment generating function (m.g.f):
See Also
Examples
dist <- dist_negative_binomial(size = 10, prob = 0.5)
dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)
support(dist)
generate(dist, 10)
density(dist, 2)
density(dist, 2, log = TRUE)
cdf(dist, 4)
quantile(dist, 0.7)