NegativeBinomial: Negative Binomial Distribution Class
In distr6: The Complete R6 Probability Distributions Interface
NegativeBinomial R Documentation
Negative Binomial Distribution Class
Description
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.
Details
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,…} 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.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on {0,1,2,…} (for fbs and sbf) or {n,n+1,n+2,…} (for tbf and tbs) (see below).
Default Parameterisation
NBinom(size = 10, prob = 0.5, form = "fbs")
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> NegativeBinomial
Public fields
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.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
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Method new()
Creates a new instance of this R6 class.
Usage
NegativeBinomial$new(
size = NULL,
prob = NULL,
qprob = NULL,
mean = NULL,
form = NULL,
decorators = NULL
)
Arguments
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 $description to see the Negative Binomial form.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
NegativeBinomial$mean(...)
Arguments
...Unused.
Method 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).
Usage
NegativeBinomial$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
Method variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.
Usage
NegativeBinomial$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the
distribution and σ is the standard deviation of the distribution.
Usage
NegativeBinomial$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the
distribution and σ is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.
Usage
NegativeBinomial$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
Method 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.
Usage
NegativeBinomial$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
NegativeBinomial$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method 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.
Usage
NegativeBinomial$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
NegativeBinomial$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01).
Michael P. McLaughlin.
See Also
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
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| NegativeBinomial | R Documentation |
Negative Binomial Distribution Class
Description
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.
Details
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,…} 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.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on {0,1,2,…} (for fbs and sbf) or {n,n+1,n+2,…} (for tbf and tbs) (see below).
Default Parameterisation
NBinom(size = 10, prob = 0.5, form = "fbs")
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> NegativeBinomial
Public fields
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.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
Method new()
Creates a new instance of this R6 class.
Usage
NegativeBinomial$new( size = NULL, prob = NULL, qprob = NULL, mean = NULL, form = NULL, decorators = NULL )
Arguments
size(integer(1))
Number of trials/successes.prob(numeric(1))
Probability of success.qprob(numeric(1))
Probability of failure. If provided thenprobis ignored.qprob = 1 - prob.mean(numeric(1))
Mean of distribution, alternative toprobandqprob.formcharacter(1))
Form of the distribution, cannot be changed after construction. Options are to model the number of,-
"fbs"- Failures before successes. -
"sbf"- Successes before failures. -
"tbf"- Trials before failures. -
"tbs"- Trials before successes. Use$descriptionto see the Negative Binomial form.
-
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
NegativeBinomial$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Usage
NegativeBinomial$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise"all"returns all modes, otherwise specifies which mode to return.
Method 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.
Usage
NegativeBinomial$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.
Usage
NegativeBinomial$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
Usage
NegativeBinomial$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
NegativeBinomial$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method 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.
Usage
NegativeBinomial$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
NegativeBinomial$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
NegativeBinomial$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
See Also
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
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