Mathematical and statistical functions for the Poisson distribution, which is commonly used to model the number of events occurring in at a constant, independent rate over an interval of time or space.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the Naturals.
Pois(rate = 1)
N/A
N/A
distr6::Distribution
-> distr6::SDistribution
-> Poisson
name
Full name of distribution.
short_name
Short name of distribution for printing.
description
Brief description of the distribution.
packages
Packages required to be installed in order to construct the distribution.
new()
Creates a new instance of this R6 class.
Poisson$new(rate = NULL, decorators = NULL)
rate
(numeric(1))
Rate parameter of the distribution, defined on the positive Reals.
decorators
(character())
Decorators to add to the distribution during construction.
mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.
Poisson$mean(...)
...
Unused.
mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Poisson$mode(which = "all")
which
(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all"
returns all modes, otherwise specifies
which mode to return.
variance()
The variance of a distribution is defined by the formula $$var_X = E[X^2] - E[X]^2$$ where \(E_X\) is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Poisson$variance(...)
...
Unused.
skewness()
The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.
Poisson$skewness(...)
...
Unused.
kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
Poisson$kurtosis(excess = TRUE, ...)
excess
(logical(1))
If TRUE
(default) excess kurtosis returned.
...
Unused.
mgf()
The moment generating function is defined by $$mgf_X(t) = E_X[exp(xt)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.
Poisson$mgf(t, ...)
t
(integer(1))
t integer to evaluate function at.
...
Unused.
cf()
The characteristic function is defined by $$cf_X(t) = E_X[exp(xti)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.
Poisson$cf(t, ...)
t
(integer(1))
t integer to evaluate function at.
...
Unused.
pgf()
The probability generating function is defined by $$pgf_X(z) = E_X[exp(z^x)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.
Poisson$pgf(z, ...)
z
(integer(1))
z integer to evaluate probability generating function at.
...
Unused.
clone()
The objects of this class are cloneable with this method.
Poisson$clone(deep = FALSE)
deep
Whether to make a deep clone.
The Poisson distribution parameterised with arrival rate, \(\lambda\), is defined by the pmf, $$f(x) = (\lambda^x * exp(-\lambda))/x!$$ for \(\lambda\) > 0.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other continuous distributions:
Arcsine
,
BetaNoncentral
,
Beta
,
Cauchy
,
ChiSquaredNoncentral
,
ChiSquared
,
Dirichlet
,
Erlang
,
Exponential
,
FDistributionNoncentral
,
FDistribution
,
Frechet
,
Gamma
,
Gompertz
,
Gumbel
,
InverseGamma
,
Laplace
,
Logistic
,
Loglogistic
,
Lognormal
,
MultivariateNormal
,
Normal
,
Pareto
,
Rayleigh
,
ShiftedLoglogistic
,
StudentTNoncentral
,
StudentT
,
Triangular
,
Uniform
,
Wald
,
Weibull
Other univariate distributions:
Arcsine
,
Bernoulli
,
BetaNoncentral
,
Beta
,
Binomial
,
Categorical
,
Cauchy
,
ChiSquaredNoncentral
,
ChiSquared
,
Degenerate
,
DiscreteUniform
,
Empirical
,
Erlang
,
Exponential
,
FDistributionNoncentral
,
FDistribution
,
Frechet
,
Gamma
,
Geometric
,
Gompertz
,
Gumbel
,
Hypergeometric
,
InverseGamma
,
Laplace
,
Logarithmic
,
Logistic
,
Loglogistic
,
Lognormal
,
Matdist
,
NegativeBinomial
,
Normal
,
Pareto
,
Rayleigh
,
ShiftedLoglogistic
,
StudentTNoncentral
,
StudentT
,
Triangular
,
Uniform
,
Wald
,
Weibull
,
WeightedDiscrete