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.

## Value

Returns an R6 object inheriting from class SDistribution.

## 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).

## 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)))

N/A

N/A

## References

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, 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

## Super classes

distr6::Distribution -> distr6::SDistribution -> Arrdist

## Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

alias

Alias of the distribution.

## Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

## Methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

#### 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).

### 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).

#### 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).

#### 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.

#### 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).

#### 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.

Arrdist$clone(deep = FALSE) #### Arguments deep Whether to make a deep clone. ## Examples x <- Arrdist$new(pdf = array(0.5, c(3, 2, 4),
dimnames = list(NULL, 1:2, NULL)))
Arrdist$new(cdf = array(c(0.5, 0.5, 0.5, 1, 1, 1), c(3, 2, 4), dimnames = list(NULL, 1:2, NULL))) # equivalently #> Arrdist(3x2x4) # d/p/q/r x$pdf(1)
#>   [,1] [,2] [,3]
#> 1  0.5  0.5  0.5
x$cdf(1:2) # Assumes ordered in construction #> [,1] [,2] [,3] #> 1 0.5 0.5 0.5 #> 2 1.0 1.0 1.0 x$quantile(0.42) # Assumes ordered in construction
#>      [,1] [,2] [,3]
#> [1,]    1    1    1
x$rand(10) #> [,1] [,2] [,3] #> [1,] 2 1 2 #> [2,] 1 2 1 #> [3,] 1 2 1 #> [4,] 2 2 2 #> [5,] 2 2 1 #> [6,] 2 2 1 #> [7,] 2 2 2 #> [8,] 2 2 1 #> [9,] 1 2 1 #> [10,] 1 1 1 # Statistics x$mean()
#> [1] 1.5 1.5 1.5
x$variance() #> [1] 0.25 0.25 0.25 summary(x) #> Array Probability Distribution. #> Parameterised with: #> #> Id Support #> <char> <char> #> 1: cdf [0,1]^n #> 2: pdf [0,1]^n #> 3: which.curve {mean} ∪ ℤ ∪ (0,1) #> 4: x ℤ #> Value #> <list> #> 1: #> 2: 0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,... #> 3: 0.5 #> 4: #> Tags #> <list> #> 1: required,linked #> 2: required,linked #> 3: required #> 4: immutable #> #> #> Quick Statistics #> Mean: 1.5, 1.5, 1.5 #> Variance: 0.25, 0.25, 0.25 #> Skewness: 000 #> Ex. Kurtosis: -2-2-2 #> #> Support: {1, 2} Scientific Type: ℝ^n #> #> Traits: discrete; univariate #> Properties: asymmetric; platykurtic platykurtic platykurtic; no skew no skew no skew # Changing which.curve arr <- array(runif(90), c(3, 2, 5), list(NULL, 1:2, NULL)) arr <- aperm(apply(arr, c(1, 3), function(x) x / sum(x)), c(2, 1, 3)) arr[, , 1:3] #> , , 1 #> #> 1 2 #> [1,] 0.04677327 0.9532267 #> [2,] 0.32013436 0.6798656 #> [3,] 0.41040922 0.5895908 #> #> , , 2 #> #> 1 2 #> [1,] 0.7650905 0.2349095 #> [2,] 0.5823992 0.4176008 #> [3,] 0.2655225 0.7344775 #> #> , , 3 #> #> 1 2 #> [1,] 0.45597150 0.5440285 #> [2,] 0.46175050 0.5382495 #> [3,] 0.08836011 0.9116399 #> x <- Arrdist$new(arr)
x$mean() # default 0.5 quantile (in this case index 3) #> [1] 1.544029 1.417601 1.634341 x$setParameterValue(which.curve = 3) # equivalently
x$mean() #> [1] 1.544029 1.538250 1.911640 # 1% quantile x$setParameterValue(which.curve = 0.01)
x$mean() #> [1] 0.5319016 0.4988487 1.1706783 # 5th index x$setParameterValue(which.curve = 5)
x$mean() #> [1] 1.591033 1.077222 1.634341 # mean x$setParameterValue(which.curve = "mean")
x\$mean()
#> [1] 1.513675 1.404545 1.681100