generate data from arbitrary probability random function

HI,

I Have a arbitrary probility function and I want to generate data according to this function

my function is:

f=7.6*exp(-2.1*x)+1.6*exp(-1.8*x)*cos(2.2*x+1.3)+9.4*exp(-2.04*x)*cos(x-2.6)

how can I generate data from this probability density function?

if I generate this data I would like to plot histogram of the generated data.

[Bruno Luong]

pdf not propertly normalized

f = @(x)7.6*exp(-2.1*x)+1.6*exp(-1.8*x).*cos(2.2*x+1.3)+9.4*exp(-2.04*x).*cos(x-2.6);
integral(f,0,100)

returns

   1.0500

[Bruno Luong]

And in addition pdf is negative

>> y=f(linspace(0,10));
>> min(y)

ans =

   -0.0268

>> 

[Torsten]

Most probably, the coefficients in f are rounded.

[hamidreza hamidi]

I estimated this function and x is between 0 and 20

Answer 1

[Torsten]

n = 1000;
ur = zeros(n,1);
u = rand(n,1);
f = @(x)7.6*exp(-2.1*x)+1.6*exp(-1.8*x).*cos(2.2*x+1.3)+9.4*exp(-2.04*x).*cos(x-2.6);
for i = 1:numel(u)
  fun = @(x)integral(f,0,x)-u(i);
  ur(i) = fzero(fun,0.5);
end
histogram(ur)

[hamidreza hamidi]

can I have an interval? for example data with x between 0 and 10?

[Torsten]

Adapt your probability function such that the integral from 0 to 10 equals 1 (e.g by dividing f(x) by integral_{0}^{10} f(x) dx).

Then the above method will produce random numbers between 0 and 10.

Best wishes

Torsten.