how to make random vector with a certain profile

Well, im looking for a way to produce a random vector that behave like the profile in the picture.

It needs to start from let's say around 2, then climbs up to a max value not higher than 20, and then drops to zero.

That is the general idea, the distribution doesnt have to be exactly like in the graph.

does anyone have a good idea how to make that happened?

[Walter Roberson]

Do you happen to have the data for that plot available? Rather than us having to read it off the graph and enter the values by hand.

[samuel]

the data is random, it is just an example.

the profile is what matter. do you still need the data? i will send it

Answer 1

[Bruno Luong]

r=linspace(0,1.5);
fv=(1.5-r).*(2+10*exp(-((r-1)./0.3).^2)); % whatever unnormaized pdf

% NOTE: This method assumes r is an equidistance vector
% otherwise you need to multiply fv by dr before cumulative sum
c = cumsum(fv);
c=(c-c(1))/(c(end)-c(1));
[cu,loc] = unique(c);
rs=r(loc);
x=interp1(cu, rs, rand(1,1e6)); % your random vector

% Check
subplot(2,1,1);
plot(r,fv);
subplot(2,1,2);
hist(x,100)

[Walter Roberson]

What is c?

[Bruno Luong]

just edit with c calculation

[samuel]

that's good, but how can i get a different output every time im running the code?

the reason is that im using different fv everytime, to build a library of results using this random fv.

[Bruno Luong]

If you want change for different pdf fv then change it, it in the line #1 & 2 of my code example.

[samuel]

actualy r is given and constant. that i can not change.

for fv (#2 line), if i play with numbers, wont it mess up the profile?

Answer 2

[Bruno Luong]

Modified code in case r is not equidistance (but monotonic)

rmid = 0.5*(r(1:end-1) + r(2:end));
dr = r(2:end)-r(1:end-1);
fvfun = @(r)(1.5-r).^3.*(2+50*exp(-((r-1)./0.3).^2)); % whatever
fv = fvfun(rmid);

c = cumsum(fv.*dr);
c = [0, c]/c(end);
[cu, loc] = unique(c);
x = interp1(cu, r(loc), rand(1,1e6));