Mathematical and statistical functions for the Negative Binomial distribution, which is commonly used to model the number of successes, trials or failures before a given number of failures or successes.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on \({0,1,2,\ldots}\) (for fbs and sbf) or \({n,n+1,n+2,\ldots}\) (for tbf and tbs) (see below).
NBinom(size = 10, prob = 0.5, form = "fbs")
N/A
N/A
distr6::Distribution -> distr6::SDistribution -> NegativeBinomial
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.
propertiesReturns distribution properties, including skewness type and symmetry.
new()Creates a new instance of this R6 class.
NegativeBinomial$new( size = NULL, prob = NULL, qprob = NULL, mean = NULL, form = NULL, decorators = NULL )
size(integer(1))
Number of trials/successes.
prob(numeric(1))
Probability of success.
qprob(numeric(1))
Probability of failure. If provided then prob is ignored. qprob = 1 - prob.
mean(numeric(1))
Mean of distribution, alternative to prob and qprob.
formcharacter(1))
Form of the distribution, cannot be changed after construction. Options are to model
the number of,
"fbs" - Failures before successes.
"sbf" - Successes before failures.
"tbf" - Trials before failures.
"tbs" - Trials before successes.
Use $description to see the Negative Binomial form.
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.
NegativeBinomial$mean(...)
...Unused.
mode()The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
NegativeBinomial$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.
NegativeBinomial$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.
NegativeBinomial$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.
NegativeBinomial$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.
NegativeBinomial$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.
NegativeBinomial$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.
NegativeBinomial$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
clone()The objects of this class are cloneable with this method.
NegativeBinomial$clone(deep = FALSE)
deepWhether to make a deep clone.
The Negative Binomial distribution parameterised with number of failures before successes, \(n\), and probability of success, \(p\), is defined by the pmf, $$f(x) = C(x + n - 1, n - 1) p^n (1 - p)^x$$ for \(n = {0,1,2,\ldots}\) and probability \(p\), where \(C(a,b)\) is the combination (or binomial coefficient) function.
The Negative Binomial distribution can refer to one of four distributions (forms):
The number of failures before K successes (fbs)
The number of successes before K failures (sbf)
The number of trials before K failures (tbf)
The number of trials before K successes (tbs)
For each we refer to the number of K successes/failures as the size parameter.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other discrete distributions:
Bernoulli,
Binomial,
Categorical,
Degenerate,
DiscreteUniform,
EmpiricalMV,
Empirical,
Geometric,
Hypergeometric,
Logarithmic,
Matdist,
Multinomial,
WeightedDiscrete
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,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete