Mathematical and statistical functions for the Matdist distribution, which is commonly used in vectorised empirical estimators such as Kaplan-Meier.

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The Matdist distribution is defined by the pmf, $$f(x_{ij}) = p_{ij}$$ for $$p_{ij}, i = 1,\ldots,k, j = 1,\ldots,n; \sum_i p_{ij} = 1$$.

#### Arguments

pdf

numeric()
Probability mass function for corresponding samples, should be same length x. If cdf is not given then calculated as cumsum(pdf).

cdf

numeric()
Cumulative distribution function for corresponding samples, should be same length x. If given then pdf calculated as difference of cdfs.

decorators

(character())
Decorators to add to the distribution during construction.

x

numeric()
Data samples, must be ordered in ascending order.

### Method strprint()

Printable string representation of the Distribution. Primarily used internally.

...

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).

#### 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).

...

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).

#### 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).

#### 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).

#### Arguments

deep

Whether to make a deep clone.

## Examples

x <- Matdist$new(pdf = matrix(0.5, 2, 2, dimnames = list(NULL, 1:2))) Matdist$new(cdf = matrix(c(0.5, 1), 2, 2, TRUE, dimnames = list(NULL, c(1, 2)))) # equivalently
#> Matdist()

# d/p/q/r
x$pdf(1:5) #> [,1] [,2] #> 1 0.5 0.5 #> 2 0.5 0.5 #> 3 0.0 0.0 #> 4 0.0 0.0 #> 5 0.0 0.0 x$cdf(1:5) # Assumes ordered in construction
#>   [,1] [,2]
#> 1  0.5  0.5
#> 2  1.0  1.0
#> 3  1.0  1.0
#> 4  1.0  1.0
#> 5  1.0  1.0
x$quantile(0.42) # Assumes ordered in construction #> [,1] [,2] #> [1,] 1 1 x$rand(10)
#>       [,1] [,2]
#>  [1,]    2    2
#>  [2,]    2    2
#>  [3,]    1    1
#>  [4,]    2    2
#>  [5,]    2    2
#>  [6,]    1    2
#>  [7,]    2    2
#>  [8,]    2    2
#>  [9,]    1    2
#> [10,]    2    2

# Statistics
x$mean() #> [1] 1.5 1.5 x$variance()
#> [1] 0.25 0.25

summary(x)
#> Matrix Probability Distribution.
#> Parameterised with:
#>
#>     Id Support           Value            Tags
#> 2: pdf [0,1]^n 0.5,0.5,0.5,0.5 required,linked
#> 3:   x       ℤ                       immutable
#>
#>
#> Quick Statistics
#> 	Mean:		1.5, 1.5
#> 	Variance:	0.25, 0.25
#> 	Skewness:	00
#> 	Ex. Kurtosis:	-2-2
#>
#> Support: {1, 2} 	Scientific Type: ℝ^n
#>
#> Traits:		discrete; univariate
#> Properties:	asymmetric; platykurtic platykurtic; no skew no skew