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 <savicky@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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