empiricalC: The Continuous Empirical Distribution

Description Usage Arguments Details Value See Also Examples

Description

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

Usage

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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.

p

Vector of probabilities.

n

Number of random values. If length(n) > 1, the length is taken to be the number required.

min

A finite minimal value.

max

A finite maximal value.

values

Vector of numerical values.

prob

Optionnal vector of count 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].

Details

Given p_i, the distribution value for x_i with i the rank i = 0, 1, 2, …, N+1, x_0 = min and x_(N+1) = max the density is:

f(x) = p_i + (p_(i+1) - p_i)/(x_(i+1) - x_i) for x_i<=x<x_(i+1)

The p values being 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 matrixes, 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 of x, q, p or random value, ... Recycling is permitted if the number of elements of min or max or the number of rows of prob and values are equal or equals 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

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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))
## the first x apply to the first row 
## the second x to the second one
dempiricalC(c(1, 1), values, min=0, max=11)


##Use with mc2d 
val <- c(100, 150, 170, 200)
pr <- c(6, 12, 6, 6)
out <- c("min", "mean", "max")
##First Bootstrap in the uncertainty dimension
##with rempirical D
(x <- mcstoc(rempiricalD, type = "U", outm = out, nvariates = 30, values = val, prob = pr))
##Continuous Empirical distribution in the variability dimension
mcstoc(rempiricalC, type = "VU", values = x, min=90, max=210)

mc2d documentation built on July 5, 2021, 5:09 p.m.