empiricalC: The Continuous Empirical Distribution

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

The Continuous Empirical Distribution

Description

Density, distribution function, quantile function and random generation for a continuous empirical distribution.

Usage

dempiricalC(x, min, max, values, prob = NULL, log = FALSE)

pempiricalC(q, min, max, values, prob = NULL, lower.tail = TRUE, log.p = FALSE)

qempiricalC(p, min, max, values, prob = NULL, lower.tail = TRUE, log.p = FALSE)

rempiricalC(n, min, max, values, prob = NULL)

Arguments

x, q	vector of quantiles.
min	a finite minimal value.
max	a finite maximal value.
values	vector of numerical values.
prob	optional vector of counts or probabilities.
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

Given p_{i}, the distribution value for x_{i} with ‘⁠i⁠’ the rank i = 0, 1, 2, \ldots, N+1, x_{0}=min and x_{N+1}=max, the density is:

f(x)=p_{i}+\frac{(p_{i+1}-p_{i})(x-x_{i})}{x_{i+1}-x_{i}}

The ‘⁠p⁠’ values are normalized to give the distribution a unit area.

‘⁠min⁠’ and/or ‘⁠max⁠’ and/or ‘⁠values⁠’ and/or ‘⁠prob⁠’ may vary: in that case, ‘⁠min⁠’ and/or ‘⁠max⁠’ should be vector(s). ‘⁠values⁠’ and/or ‘⁠prob⁠’ should be 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 elements of ‘⁠min⁠’ or ‘⁠max⁠’ or the number of rows of ‘⁠prob⁠’ and ‘⁠values⁠’ are equal or equal to one.

Value

‘⁠dempiricalC⁠’ gives the density, ‘⁠pempiricalC⁠’ gives the distribution function, ‘⁠qempiricalC⁠’ gives the quantile function and ‘⁠rempiricalC⁠’ generates random deviates.

See Also

empiricalD

Examples

prob <- c(2, 3, 1, 6, 1)
values <- 1:5
par(mfrow = c(1, 2))
curve(dempiricalC(x, min=0, max=6, values, prob), from=-1, to=7, n=1001)
curve(pempiricalC(x, min=0, max=6, values, prob), from=-1, to=7, n=1001)

## Varying values
(values <- matrix(1:10, ncol=5))
dempiricalC(c(1, 1), values, min=0, max=11)

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