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
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages 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)
deepWhether 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