Draw random number from a truncated distribution with upper bound

Hello everyone,

how can I draw a random number from a truncated normal distribution with mean 0 and varying var (sigma^2)? The upper bound of the truncation value varies within my time series. What I did first is to specify the probability distribution for the different variance values (1xn matrix). After that, I draw a truncated normal distribution for each "row"/ new upper bound. Since I have a huge time series, this step takes forever.

for i = 1:size(pd,2);
t(:,i) = truncate(pd(size(pd,1),i),-inf,upperBound(:,i)));
end

Whenever, this step would be executed I would draw a random number out of each truncated distribution, using

r = random(t(:,1),1);

However, I am not sure if that will work, though.

Is there a way to predefine the matrix for the specification of t? A normal zero/nan etc. matrix doesnt work. And how can I speed up the process to draw from a truncated normal distribution with varying upper bound values?

Answer 1

[Torsten]

https://de.mathworks.com/matlabcentral/fileexchange/53180-truncated-normal-generator

Best wishes

Torsten.

[Leo]

Thanks you! But I already tried this function but I dont know what I am doing wrong.

Some of the drawn numbers are still greater than the upper bound. This is the normal code that I am using:

trunc = trandn((l - m) ./ s ,(u - m) ./ s) ;

where s is the varying standard deviation.

I construct a matrix

truncM = vec2mat(trunc,5);

and then "generate" the truncated random number by

   r = (s .* truncM) + m ;

Do you know what I might be doing wrong?

Thank you in advance!

[Torsten]

What are the sizes of l, u, m and s ?

Best wishes

Torsten.

[Leo]

• u = upper bound is 605000 x 5
• l = the value of the lower bound is set to infinite and is also a 605000 x 5, to match the sizes
• m = is a scalar and is equal to zero and s = 1x5, but to match the sizes, I use repmat to obtain a 605000x5 matrix

Thanks!

[Torsten]

u=10;
s=1;
m=3;
U=normcdf(u);

n=100;
X=rand(n,1);
Y=m+s*norminv(X*U);

produces n random numbers taken from the normal distribution N(m,s^2) truncated at the upper bound u.

Can you take it from here ?

Best wishes

Torsten.

[Leo]

Thank you for your help. I finally got trandn to work properly. I added some for loops. Your 2nd suggestion did also work fine. Thanks a lot!