Hi Petr,
Thank you very much. It looks we are almost there.
#an example, use a function approximating your graphs
* f <- function(x) { 0.7 - 1.25*((x - 1)^2 - 0.4)^2 }
f <- function(x) { 0.2 - 1.5*((x - 1)^2 - 0.1)^2 }
#plot function f(x)
# x <- seq(0, 2, length=51)
x <- seq(0.01, 1.75, length=51)
y <- f(x)
plot(x, y, type="l")
The above plot may give the desired result.
Here are the the conditions.
1. Y- value is always positive.
2. Can I set the mean and SD of the value of X?
Example mean of x= 24 and SD =5
Thanks
On Wed, Feb 1, 2012 at 6:20 AM, Petr Savicky <savi...@cs.cas.cz> wrote:
> On Tue, Jan 31, 2012 at 01:59:13PM -0500, Val wrote:
> > Hi petr,
> >
> > >Can the required density be understood as a piecewise
> > >linear function going through 4 or 5 given points?
> >
> > That is my problem. The function should be nonlinear. However, we can
> break
> > it down to the first 3 or 4 points could be linear and then nonlinear
> > function. On the later points can we apply sort of spline function or
> local
> > polynomials?
>
> Hi.
>
> The following is a simpler solution, where we can start
> with a function f(x), which is a multiple of the required
> density, so it specifies its shape.
>
> #an example, use a function approximating your graphs
> f <- function(x) { 0.7 - 1.25*((x - 1)^2 - 0.4)^2 }
>
> #plot function f(x)
> x <- seq(0, 2, length=51)
> y <- f(x)
> plot(x, y, type="l")
>
> #plot an approximate distribution function
> xDistr <- x
> yDistr <- cumsum(y)/sum(y)
> plot(xDistr, yDistr, type="l")
>
> #generate random sample
> library(splines)
> invDistr <- interpSpline(yDistr, xDistr)
> z <- predict(invDistr, runif(100000))$y
>
> #plot the empirical distribution function
> lines(sort(z), seq(0, 1, length=length(z)), col=2)
>
> #for a more accurate comparison subtract the line with slope 1/2
> plot(xDistr, yDistr - xDistr/2, type="l")
> lines(sort(z), seq(0, 1, length=length(z)) - sort(z)/2, col=2)
>
> Hope this helps.
>
> Petr.
>
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