Arrdist: Arrdist Distribution Class
In RaphaelS1/distr6: The Complete R6 Probability Distributions Interface
Arrdist R Documentation
Arrdist Distribution Class
Description
Mathematical and statistical functions for the Arrdist distribution, which
is commonly used in matrixed Bayesian estimators such as Kaplan-Meier with confidence bounds over arbitrary dimensions.
Details
The Arrdist distribution is defined by the pmf,
f(x_{ijk}) = p_{ijk}
for p_{ijk}, i = 1,\ldots,a, j = 1,\ldots,b; \sum_i p_{ijk} = 1.
This is a generalised case of Matdist with a third dimension over an arbitrary length.
By default all results are returned for the median curve as determined by
(dim(a)[3L] + 1)/2 where a is the array and assuming third dimension is odd,
this can be changed by setting the which.curve parameter.
Given the complexity in construction, this distribution is not mutable (cannot be updated after construction).
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on x_{111},...,x_{abc}.
Default Parameterisation
Arrdist(array(0.5, c(2, 2, 2), list(NULL, 1:2, NULL)))
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> Arrdist
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$getParameterValue()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$setParameterValue()distr6::Distribution$stdev()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class.
Usage
Arrdist$new(pdf = NULL, cdf = NULL, which.curve = 0.5, decorators = NULL)
Arguments
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 calculated as difference of cdfs.
which.curvenumeric(1) | character(1)
Which curve (third dimension) should results be displayed for? If
between (0,1) taken as the quantile of the curves otherwise if greater than 1 taken as the curve index, can also be 'mean'. See examples.
decorators(character())
Decorators to add to the distribution during construction.
Method strprint()
Printable string representation of the Distribution. Primarily used internally.
Usage
Arrdist$strprint(n = 2)
Arguments
n(integer(1))
Ignored.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
If distribution is improper (F(Inf) != 1, then E_X(x) = Inf).
Usage
Arrdist$mean(...)
Arguments
...Unused.
Method median()
Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns self$mean, otherwise
returns self$quantile(0.5).
Usage
Arrdist$median()
Method mode()
The mode of a probability distribution is the point at which the pdf is
a local maximum, a distribution can be unimodal (one maximum) or multimodal (several
maxima).
Usage
Arrdist$mode(which = 1)
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
Arrdist$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
If distribution is improper (F(Inf) != 1, then sk_X(x) = Inf).
Usage
Arrdist$skewness(...)
Arguments
...Unused.
Method 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.
If distribution is improper (F(Inf) != 1, then k_X(x) = Inf).
Usage
Arrdist$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
If distribution is improper then entropy is Inf.
Usage
Arrdist$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
Arrdist$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
If distribution is improper (F(Inf) != 1, then cf_X(x) = Inf).
Usage
Arrdist$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
Arrdist$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
Arrdist$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,
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,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
Examples
x <- Arrdist$new(pdf = array(0.5, c(3, 2, 4),
dimnames = list(NULL, 1:2, NULL)))
Arrdist$new(cdf = array(c(0.5, 0.5, 0.5, 1, 1, 1), c(3, 2, 4),
dimnames = list(NULL, 1:2, NULL))) # equivalently
# d/p/q/r
x$pdf(1)
x$cdf(1:2) # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)
# Statistics
x$mean()
x$variance()
summary(x)
# Changing which.curve
arr <- array(runif(90), c(3, 2, 5), list(NULL, 1:2, NULL))
arr <- aperm(apply(arr, c(1, 3), function(x) x / sum(x)), c(2, 1, 3))
arr[, , 1:3]
x <- Arrdist$new(arr)
x$mean() # default 0.5 quantile (in this case index 3)
x$setParameterValue(which.curve = 3) # equivalently
x$mean()
# 1% quantile
x$setParameterValue(which.curve = 0.01)
x$mean()
# 5th index
x$setParameterValue(which.curve = 5)
x$mean()
# mean
x$setParameterValue(which.curve = "mean")
x$mean()
RaphaelS1/distr6 documentation built on Feb. 24, 2024, 9:14 p.m.
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| Arrdist | R Documentation |
Arrdist Distribution Class
Description
Mathematical and statistical functions for the Arrdist distribution, which is commonly used in matrixed Bayesian estimators such as Kaplan-Meier with confidence bounds over arbitrary dimensions.
Details
The Arrdist distribution is defined by the pmf,
f(x_{ijk}) = p_{ijk}
for p_{ijk}, i = 1,\ldots,a, j = 1,\ldots,b; \sum_i p_{ijk} = 1.
This is a generalised case of Matdist with a third dimension over an arbitrary length.
By default all results are returned for the median curve as determined by
(dim(a)[3L] + 1)/2 where a is the array and assuming third dimension is odd,
this can be changed by setting the which.curve parameter.
Given the complexity in construction, this distribution is not mutable (cannot be updated after construction).
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on x_{111},...,x_{abc}.
Default Parameterisation
Arrdist(array(0.5, c(2, 2, 2), list(NULL, 1:2, NULL)))
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> Arrdist
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$getParameterValue()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$setParameterValue()distr6::Distribution$stdev()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class.
Usage
Arrdist$new(pdf = NULL, cdf = NULL, which.curve = 0.5, decorators = NULL)
Arguments
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 thenpdfcalculated as difference ofcdfs.which.curvenumeric(1) | character(1)
Which curve (third dimension) should results be displayed for? If between (0,1) taken as the quantile of the curves otherwise if greater than 1 taken as the curve index, can also be 'mean'. See examples.decorators(character())
Decorators to add to the distribution during construction.
Method strprint()
Printable string representation of the Distribution. Primarily used internally.
Usage
Arrdist$strprint(n = 2)
Arguments
n(integer(1))
Ignored.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions. If distribution is improper (F(Inf) != 1, then E_X(x) = Inf).
Usage
Arrdist$mean(...)
Arguments
...Unused.
Method median()
Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns self$mean, otherwise
returns self$quantile(0.5).
Usage
Arrdist$median()
Method mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Usage
Arrdist$mode(which = 1)
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
Arrdist$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
If distribution is improper (F(Inf) != 1, then sk_X(x) = Inf).
Usage
Arrdist$skewness(...)
Arguments
...Unused.
Method 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.
If distribution is improper (F(Inf) != 1, then k_X(x) = Inf).
Usage
Arrdist$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
If distribution is improper then entropy is Inf.
Usage
Arrdist$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
Arrdist$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
If distribution is improper (F(Inf) != 1, then cf_X(x) = Inf).
Usage
Arrdist$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
Arrdist$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
Arrdist$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,
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,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
Examples
x <- Arrdist$new(pdf = array(0.5, c(3, 2, 4),
dimnames = list(NULL, 1:2, NULL)))
Arrdist$new(cdf = array(c(0.5, 0.5, 0.5, 1, 1, 1), c(3, 2, 4),
dimnames = list(NULL, 1:2, NULL))) # equivalently
# d/p/q/r
x$pdf(1)
x$cdf(1:2) # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)
# Statistics
x$mean()
x$variance()
summary(x)
# Changing which.curve
arr <- array(runif(90), c(3, 2, 5), list(NULL, 1:2, NULL))
arr <- aperm(apply(arr, c(1, 3), function(x) x / sum(x)), c(2, 1, 3))
arr[, , 1:3]
x <- Arrdist$new(arr)
x$mean() # default 0.5 quantile (in this case index 3)
x$setParameterValue(which.curve = 3) # equivalently
x$mean()
# 1% quantile
x$setParameterValue(which.curve = 0.01)
x$mean()
# 5th index
x$setParameterValue(which.curve = 5)
x$mean()
# mean
x$setParameterValue(which.curve = "mean")
x$mean()
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