Generate random numbers with truncated Pareto distribution

I am wanting to generate a series of random numbers from a truncated Pareto distribution. I can see there is a function in matlab for a generalized pareto, but is there a way to do a truncated Pareto?

[Torsten]

Could you include the cumulative distribution function of the truncated Pareto distribution you are talking about ?

Is it

F(x) = (1-(a/x)^c) / (1-(a/b)^c)

for a <= x <= b ?

Answer 1

[David Hill]

Just write a simple function

function x = ranPareto_trunc(H,L,alpha,n)%H=upper, L=lower, alpha>0, n=number of random numbers desired
u=rand(1,n);
x=(-(u*H^alpha-u*L^alpha-H^alpha)/H^alpha/L^alpha).^(-1/alpha);
end

Answer 2

[Bruno Luong]

According the https://en.wikipedia.org/wiki/Pareto_distribution

the pareto has bounded on the lower side by what they called xm.

So I introduce the upper bound

% up > xm

For the shape parameter alpha, r is N realization of conditiona pareto probability distribution such that r < up (bounded or truncated pareto) can be obtained as following

alpha = 2; % % distribution tail index parameter
xm = 1; % lower bound
up = 3; % upper bound
N = 1e6;

% Generate by method of inverse of cdf
a = 1-(xm/up)^alpha;
r = (1-a*rand(1,N)).^(-1/alpha)*xm;

% Graphic check
histogram(r, 'Normalization', 'pdf')