Mathematical and statistical functions for the Binomial distribution, which is commonly used to model the number of successes out of a number of independent trials.
Returns an R6 object inheriting from class SDistribution.
The Binomial distribution parameterised with number of trials, n, and probability of success, p, is defined by the pmf, $$f(x) = C(n, x)p^x(1-p)^{n-x}$$ for \(n = 0,1,2,\ldots\) and probability \(p\), where \(C(a,b)\) is the combination (or binomial coefficient) function.
The distribution is supported on \({0, 1,...,n}\).
Binom(size = 10, prob = 0.5)
N/A
N/A
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other discrete distributions:
Arrdist,
Bernoulli,
Categorical,
Degenerate,
DiscreteUniform,
EmpiricalMV,
Empirical,
Geometric,
Hypergeometric,
Logarithmic,
Matdist,
Multinomial,
NegativeBinomial,
WeightedDiscrete
Other univariate distributions:
Arcsine,
Arrdist,
Bernoulli,
BetaNoncentral,
Beta,
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,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
distr6::Distribution -> distr6::SDistribution -> Binomial
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
propertiesReturns distribution properties, including skewness type and symmetry.
Inherited methods
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$workingSupport()
new()Creates a new instance of this R6 class.
Binomial$new(size = NULL, prob = NULL, qprob = NULL, decorators = NULL)size(integer(1))
Number of trials, defined on the positive Naturals.
prob(numeric(1))
Probability of success.
qprob(numeric(1))
Probability of failure. If provided then prob is ignored. qprob = 1 - prob.
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.
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).
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.
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.
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.
entropy()The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where \(f_X\) is the pdf of distribution X, with an integration analogue for continuous distributions.
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.
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.
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.