ZTPoisson {distributions3} | R Documentation |
Create a zero-truncated Poisson distribution
Description
Zero-truncated Poisson distributions are frequently used to model counts where zero observations cannot occur or have been excluded.
Usage
ZTPoisson(lambda)
Arguments
lambda |
Parameter of the underlying untruncated Poisson distribution. Can be any positive number. |
Details
We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail.
In the following, let be a zero-truncated Poisson random variable with parameter
lambda
= .
Support:
Mean:
Variance: , where
is the mean above.
Probability mass function (p.m.f.):
where is the p.m.f. of the
Poisson
distribution.
Cumulative distribution function (c.d.f.):
where is the c.d.f. of the
Poisson
distribution.
Moment generating function (m.g.f.):
Value
A ZTPoisson
object.
See Also
Other discrete distributions:
Bernoulli()
,
Binomial()
,
Categorical()
,
Geometric()
,
HurdleNegativeBinomial()
,
HurdlePoisson()
,
HyperGeometric()
,
Multinomial()
,
NegativeBinomial()
,
Poisson()
,
ZINegativeBinomial()
,
ZIPoisson()
,
ZTNegativeBinomial()
Examples
## set up a zero-truncated Poisson distribution
X <- ZTPoisson(lambda = 2.5)
X
## standard functions
pdf(X, 0:8)
cdf(X, 0:8)
quantile(X, seq(0, 1, by = 0.25))
## cdf() and quantile() are inverses for each other
quantile(X, cdf(X, 3))
## density visualization
plot(0:8, pdf(X, 0:8), type = "h", lwd = 2)
## corresponding sample with histogram of empirical frequencies
set.seed(0)
x <- random(X, 500)
hist(x, breaks = -1:max(x) + 0.5)