# The Continuous Empirical Distribution Density, distribution function and random generation for a continuous empirical distribution. ```r 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) ``` ## Examples ```r 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) ``` ## 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})f(x)= p_i + (p_(i+1) - p_i)/(x_(i+1) - x_i) for x_i<=x

empiricalC function