empiricalD: The Discrete Empirical Distribution

In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

The Discrete Empirical Distribution

Description

Density, distribution function, quantile function and random generation for a discrete empirical distribution. This function is vectorized to accept different sets of ‘⁠values⁠’ or ‘⁠prob⁠’.

Usage

dempiricalD(x, values, prob = NULL, log = FALSE)

pempiricalD(q, values, prob = NULL, lower.tail = TRUE, log.p = FALSE)

qempiricalD(p, values, prob = NULL, lower.tail = TRUE, log.p = FALSE)

rempiricalD(n, values, prob = NULL)

Arguments

x, q	vector of quantiles.
values	vector or matrix of numerical values. See details.
prob	optional vector or matrix of counts or probabilities. See details.
log, log.p	logical; if ‘⁠TRUE⁠’, probabilities ‘⁠p⁠’ are given as ‘⁠log(p)⁠’.
lower.tail	logical; if ‘⁠TRUE⁠’ (default), probabilities are ‘⁠P[X <= x]⁠’, otherwise, ‘⁠P[X > x]⁠’.
p	vector of probabilities.
n	number of random values. If ‘⁠length(n) > 1⁠’, the length is taken to be the number required.

Details

If ‘⁠prob⁠’ is missing, the discrete distribution is obtained directly from the vector of ‘⁠values⁠’, otherwise ‘⁠prob⁠’ is used to weight the values. ‘⁠prob⁠’ is normalized before use. Thus, ‘⁠prob⁠’ may be the count of each ‘⁠values⁠’. ‘⁠prob⁠’ values should be non negative and their sum should not be 0.

‘⁠values⁠’ and/or ‘⁠prob⁠’ may vary: in that case, ‘⁠values⁠’ and/or ‘⁠prob⁠’ should be sent as matrices, the first row being used for the first element of ‘⁠x⁠’, ‘⁠q⁠’, ‘⁠p⁠’ or the first random value, the second row for the second element, ... Recycling is permitted if the number of rows of ‘⁠prob⁠’ and ‘⁠values⁠’ are equal or if the number of rows of ‘⁠prob⁠’ and/or ‘⁠values⁠’ is one.

‘⁠rempiricalD(n, values, prob)⁠’ with ‘⁠values⁠’ and ‘⁠prob⁠’ as vectors is equivalent to ‘⁠sample(x=values, size=n, replace=TRUE, prob=prob)⁠’.

Value

‘⁠dempiricalD⁠’ gives the density, ‘⁠pempiricalD⁠’ gives the distribution function, ‘⁠qempiricalD⁠’ gives the quantile function and ‘⁠rempiricalD⁠’ generates random deviates.

Note

In the future, the functions should be written for non numerical values.

See Also

sample, empiricalC.

Examples

dempiricalD(1:6, 2:6, prob=c(10, 10, 70, 0, 10))
pempiricalD(1:6, 2:6, prob=c(10, 10, 70, 0, 10))
qempiricalD(seq(0, 1, 0.1), 2:6, prob=c(10, 10, 70, 0, 10))
table(rempiricalD(10000, 2:6, prob=c(10, 10, 70, 0, 10)))

## Varying values
(values <- matrix(1:10, ncol=5))
dempiricalD(c(1, 1), values)

mc2d documentation built on Oct. 23, 2026, 1:06 a.m.