WeightedDiscrete: WeightedDiscrete Distribution Class
In distr6: The Complete R6 Probability Distributions Interface
WeightedDiscrete R Documentation
WeightedDiscrete Distribution Class
Description
Mathematical and statistical functions for the WeightedDiscrete distribution, which
is commonly used in empirical estimators such as Kaplan-Meier.
Details
The WeightedDiscrete distribution is defined by the pmf,
f(x_i) = p_i
for p_i, i = 1,…,k; ∑ p_i = 1.
Sampling from this distribution is performed with the sample function with the elements given
as the x values and the pdf as the probabilities. The cdf and quantile assume that the
elements are supplied in an indexed order (otherwise the results are meaningless).
The number of points in the distribution cannot be changed after construction.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on x_1,...,x_k.
Default Parameterisation
WeightDisc(x = 1, pdf = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> WeightedDiscrete
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of 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
WeightedDiscrete$new(x = NULL, pdf = NULL, cdf = NULL, decorators = NULL)
Arguments
xnumeric()
Data samples, must be ordered in ascending order.
pdfnumeric()
Probability mass function for corresponding samples, should be same length x.
If cdf is not given then calculated as cumsum(pdf).
cdfnumeric()
Cumulative distribution function for corresponding samples, should be same length x. If
given then pdf is ignored and calculated as difference of cdfs.
decorators(character())
Decorators to add to the distribution during construction.
Method strprint()
Printable string representation of the Distribution. Primarily used internally.
Usage
WeightedDiscrete$strprint(n = 2)
Arguments
n(integer(1))
Ignored.
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.
If distribution is improper (F(Inf) != 1, then E_X(x) = Inf).
Usage
WeightedDiscrete$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is
a local maximum, a distribution can be unimodal (one maximum) or multimodal (several
maxima).
Usage
WeightedDiscrete$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.
If distribution is improper (F(Inf) != 1, then var_X(x) = Inf).
Usage
WeightedDiscrete$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the
distribution and σ is the standard deviation of the distribution.
If distribution is improper (F(Inf) != 1, then sk_X(x) = Inf).
Usage
WeightedDiscrete$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.
If distribution is improper (F(Inf) != 1, then k_X(x) = Inf).
Usage
WeightedDiscrete$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- ∑ (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
If distribution is improper then entropy is Inf.
Usage
WeightedDiscrete$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...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.
If distribution is improper (F(Inf) != 1, then mgf_X(x) = Inf).
Usage
WeightedDiscrete$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
If distribution is improper (F(Inf) != 1, then cf_X(x) = Inf).
Usage
WeightedDiscrete$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.
If distribution is improper (F(Inf) != 1, then pgf_X(x) = Inf).
Usage
WeightedDiscrete$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
WeightedDiscrete$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,
NegativeBinomial
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,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Examples
x <- WeightedDiscrete$new(x = 1:3, pdf = c(1 / 5, 3 / 5, 1 / 5))
WeightedDiscrete$new(x = 1:3, cdf = c(1 / 5, 4 / 5, 1)) # equivalently
# d/p/q/r
x$pdf(1:5)
x$cdf(1:5) # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)
# Statistics
x$mean()
x$variance()
summary(x)
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| WeightedDiscrete | R Documentation |
WeightedDiscrete Distribution Class
Description
Mathematical and statistical functions for the WeightedDiscrete distribution, which is commonly used in empirical estimators such as Kaplan-Meier.
Details
The WeightedDiscrete distribution is defined by the pmf,
f(x_i) = p_i
for p_i, i = 1,…,k; ∑ p_i = 1.
Sampling from this distribution is performed with the sample function with the elements given as the x values and the pdf as the probabilities. The cdf and quantile assume that the elements are supplied in an indexed order (otherwise the results are meaningless).
The number of points in the distribution cannot be changed after construction.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on x_1,...,x_k.
Default Parameterisation
WeightDisc(x = 1, pdf = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> WeightedDiscrete
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of 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
WeightedDiscrete$new(x = NULL, pdf = NULL, cdf = NULL, decorators = NULL)
Arguments
xnumeric()
Data samples, must be ordered in ascending order.pdfnumeric()
Probability mass function for corresponding samples, should be same lengthx. Ifcdfis not given then calculated ascumsum(pdf).cdfnumeric()
Cumulative distribution function for corresponding samples, should be same lengthx. If given thenpdfis ignored and calculated as difference ofcdfs.decorators(character())
Decorators to add to the distribution during construction.
Method strprint()
Printable string representation of the Distribution. Primarily used internally.
Usage
WeightedDiscrete$strprint(n = 2)
Arguments
n(integer(1))
Ignored.
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. If distribution is improper (F(Inf) != 1, then E_X(x) = Inf).
Usage
WeightedDiscrete$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Usage
WeightedDiscrete$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. If distribution is improper (F(Inf) != 1, then var_X(x) = Inf).
Usage
WeightedDiscrete$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. If distribution is improper (F(Inf) != 1, then sk_X(x) = Inf).
Usage
WeightedDiscrete$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. If distribution is improper (F(Inf) != 1, then k_X(x) = Inf).
Usage
WeightedDiscrete$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- ∑ (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for continuous distributions. If distribution is improper then entropy is Inf.
Usage
WeightedDiscrete$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)...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. If distribution is improper (F(Inf) != 1, then mgf_X(x) = Inf).
Usage
WeightedDiscrete$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X. If distribution is improper (F(Inf) != 1, then cf_X(x) = Inf).
Usage
WeightedDiscrete$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. If distribution is improper (F(Inf) != 1, then pgf_X(x) = Inf).
Usage
WeightedDiscrete$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
WeightedDiscrete$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,
NegativeBinomial
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,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Examples
x <- WeightedDiscrete$new(x = 1:3, pdf = c(1 / 5, 3 / 5, 1 / 5)) WeightedDiscrete$new(x = 1:3, cdf = c(1 / 5, 4 / 5, 1)) # equivalently # d/p/q/r x$pdf(1:5) x$cdf(1:5) # Assumes ordered in construction x$quantile(0.42) # Assumes ordered in construction x$rand(10) # Statistics x$mean() x$variance() summary(x)
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