empiricalC: The Continuous Empirical Distribution

Description

Density, distribution 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)

Value

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

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: Optional 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 $i = 0, 1, 2, \ldots, N+1$, $x_{0}=min$ and $x_{N+1}=max$ the density is: $$f(x)=p_{i}+(\frac{x-x_{i}}{x_{i+1}-x_{i}})(p_{i+1}-p_{i})$$ 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.

Examples

Run this code

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)