Mathematical and statistical functions for the EmpiricalMV distribution, which is commonly used in sampling such as MCMC.

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The EmpiricalMV distribution is defined by the pmf, $$p(x) = \sum I(x = x_i) / k$$ for $$x_i \epsilon R, i = 1,...,k$$.

Sampling from this distribution is performed with the sample function with the elements given as the support set and uniform probabilities. Sampling is performed with replacement, which is consistent with other distributions but non-standard for Empirical distributions. Use simulateEmpiricalDistribution to sample without replacement.

The cdf assumes that the elements are supplied in an indexed order (otherwise the results are meaningless).

## Distribution support

The distribution is supported on $$x_1,...,x_k$$.

## Default Parameterisation

EmpMV(data = data.frame(1, 1))

N/A

N/A

## References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

## Super classes

distr6::Distribution -> distr6::SDistribution -> EmpiricalMV

## 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.

## Methods

### Public methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

### 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.

...

Unused.

### Method setParameterValue()

Sets the value(s) of the given parameter(s).

#### Arguments

deep

Whether to make a deep clone.

## Examples

## ------------------------------------------------
## Method EmpiricalMV$new ## ------------------------------------------------ EmpiricalMV$new(MultivariateNormal$new()$rand(100))
#> EmpMV(data = list(V1 = c(-0.526692630351283, -2.49536480915438, 0.350492383702827, 0.765906802532555, -0.136943428599099, 1.51974446834724, -0.0536715061508017, -0.743908962797543, -0.560829227031403, 0.748850942267306, 0.236095846759048, 0.417925675737717, -0.506286298229541, -0.948705722886941, -0.795201560474224, -1.22245109721962, -1.48926081390287, -0.942554006091392, 1.33644679792075, 0.666537819756823, 1.17005616766354, 1.10170809633169, -0.864349802977735, -0.0370514646718219, -0.499355411832378, -0.174245957308514,
#> -0.945985005280397, 0.876913144878748, -1.13761275625578, -0.494143476387761, 0.791534123645639, 0.612722103889784, 0.88862899272379, 0.22533951485482, -1.22248707000132, -0.7510122231567, 0.352010126334829, 0.104662226933443, -0.61104608224538, 0.534803326058771, -1.22250157411617, 0.465165158411011, -0.130264800618813, -0.364851004324683, 0.413154817794422, -2.17995674203001, -0.357528324755672, -0.0501418010657054, -0.632587542022358, -0.235475907427546, -1.50338214597175, -0.753198229350471,
#> 1.00578284651542, 2.3225565395417, 0.0488144355095131, -0.785235068436928, 0.68187803211519, -1.51060172429041, -2.02291845445234, 0.550015549139052, 0.893165019997801, 0.605884808224899, -0.520796372779794, -0.63589413738825, 1.17691424810852, 2.27295476618215, -1.99903913349767, -0.378407395180984, -1.5410302916367, -0.0201081842355959, 0.88986535907593, 0.445750348302804, -0.0201100267710495, 0.264661744879649, -0.183388482515322, -0.186553842004526, -1.6405816724151, 1.75433696088715, 1.01671328819622,
#> -1.07806726465165, -0.52964367726925, -0.202447558737144, -1.03377323651804, -0.046400637310866, 0.416260797910689, 0.0639187530308365, 0.901335290053489, 0.668221203714885, 0.128688091789133, 0.202360673484458, 0.361694761427865, 0.372698962423058, -0.0516945386722141, 0.549899522976571, 0.684360080826633, -1.78436472417652, 0.830147723263884, -0.122186361074584, -0.961276679679037, -0.545401573002851), V2 = c(-0.0951349075760237, 0.166889216632368, 1.43370100928187, 1.16752066984205, -0.514902043516776,
#> -0.328491677605083, -0.563524634833966, -0.109041651464962, 0.188001548963977, -1.91653831649921, 0.628953415243992, 1.97675847664655, -1.10996885267932, 0.476843756716056, 0.234326922506296, -2.45364735388403, -0.432147734134632, -0.121450799414898, -0.860356181774122, -1.42153474570427, -1.40471454250678, 0.697986262544779, -1.09147035108868, 0.810053792383895, 0.948031587815801, -1.10623595233741, 0.289089591304068, -1.14890393973024, -1.43724673508534, 0.840801808081863, -0.168848948069648, -0.771158924361937,
#> 0.0132144768460245, -0.729915209602175, 0.406805171157349, -0.162116540339154, -0.28905829997927, 0.720186530653959, -1.10691407158303, 0.736067967856697, 1.02141530978363, 0.790472704523132, -0.930285333605259, 0.153872493250671, 2.4808233597049, 0.420874577554014, -0.646861513586719, 0.416942846990301, 1.15014667345879, -1.64310738628558, -2.05058484718271, -0.134141958474824, 2.16718679846135, -1.02042339064488, -0.771888628161592, -0.726603030794874, -0.229843287173231, -0.583727687120599, 0.403504676138385,
#> 0.0283571217755485, -0.376555495773104, -0.00487472568702639, -0.639018597908028, 0.106586975364598, 0.447391153397406, 0.136058206021325, -0.420500870203527, 1.22077478856746, -0.310310122156193, -2.3902003364285, -1.48281332468633, 1.36977585585092, -0.109217587430481, 0.303848263845439, 0.559649672136207, -0.81227537165771, 0.507922477794402, 0.59240020189409, 0.121620585744186, -1.14356571956783, -0.681273155856935, 1.68449572050523, -0.155976673321198, -0.953628726504224, 0.114029609050454,
#> -0.919332238270361, -0.79772829746059, 0.155214295636058, -1.53306545321898, -0.717538652532261, 1.39900429351273, -1.56564429428522, 0.514082103022085, 0.867816913024197, -0.162679977016422, -1.03714556605811, 0.60734694486578, 0.933125139463173, 0.255081706598915, 0.930360735887222)))