Geometric {distributions3} | R Documentation |
The Geometric distribution can be thought of as a generalization
of the Bernoulli()
distribution where we ask: "if I keep flipping a
coin with probability p
of heads, what is the probability I need
k
flips before I get my first heads?" The Geometric
distribution is a special case of Negative Binomial distribution.
Geometric(p = 0.5)
p |
The success probability for the distribution. |
We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail and much greater clarity.
In the following, let X
be a Geometric random variable with
success probability p
= p
. Note that there are multiple
parameterizations of the Geometric distribution.
Support: 0 < p < 1, x = 0, 1, \dots
Mean: \frac{1-p}{p}
Variance: \frac{1-p}{p^2}
Probability mass function (p.m.f):
P(X = x) = p(1-p)^x,
Cumulative distribution function (c.d.f):
P(X \le x) = 1 - (1-p)^{x+1}
Moment generating function (m.g.f):
E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t}
A Geometric
object.
Other discrete distributions:
Bernoulli()
,
Binomial()
,
Categorical()
,
HurdleNegativeBinomial()
,
HurdlePoisson()
,
HyperGeometric()
,
Multinomial()
,
NegativeBinomial()
,
Poisson()
,
ZINegativeBinomial()
,
ZIPoisson()
,
ZTNegativeBinomial()
,
ZTPoisson()
set.seed(27)
X <- Geometric(0.3)
X
random(X, 10)
pdf(X, 2)
log_pdf(X, 2)
cdf(X, 4)
quantile(X, 0.7)