Poisson | R Documentation |
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.
The Poisson distribution parameterised with arrival rate, \lambda
, is defined by the pmf,
f(x) = (\lambda^x * exp(-\lambda))/x!
for \lambda
> 0.
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.
alias
Alias of the distribution.
packages
Packages required to be installed in order to construct the distribution.
distr6::Distribution$cdf()
distr6::Distribution$confidence()
distr6::Distribution$correlation()
distr6::Distribution$getParameterValue()
distr6::Distribution$iqr()
distr6::Distribution$liesInSupport()
distr6::Distribution$liesInType()
distr6::Distribution$median()
distr6::Distribution$parameters()
distr6::Distribution$pdf()
distr6::Distribution$prec()
distr6::Distribution$print()
distr6::Distribution$quantile()
distr6::Distribution$rand()
distr6::Distribution$setParameterValue()
distr6::Distribution$stdev()
distr6::Distribution$strprint()
distr6::Distribution$summary()
distr6::Distribution$workingSupport()
new()
Creates a new instance of this R6 class.
Poisson$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.
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
,
Arrdist
,
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
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