Simulate a custom function in Matlab - matlab

Question

I'd like to simulate the following function:
l(t) = mu + Σ (1 + (t-t_i)/alpha)^(beta)
I wrote the function as follow:
function[l] = custom(m,t,H,par)
k = length(H);
n = length(t);
l = par.mu(m)*ones(n,1);
for i = 1:n
for j = 1:k
h = H{j};
h = h(h < t(i));
if ~isempty(h)
d = t(i) - h;
l(i) = l(i) + sum((1+ (d/par.alpha(m,j)))^ par.beta(m,j));
end
end
end
Now, how can I simulate this function for t=1000, par.mu= 0.5, par.alpha = 0.1, par.beta = 0.3?
I have the following code for simulation of this function but it's not efficient...How can I make it better?
function[h] = simcustom(t,par)
h = -log(rand)/par.mu;
if h < t
do5 = 1;
i = 0;
j = 0;
k = 0;
n = 1;
while true
if do5;
k = k + 1;
Lstar(k) = custom(1,h(n),{h},par); %#ok
end
j = j + 1;
U(j) = rand; %#ok
i = i + 1;
u(i) = -log(U(j))/Lstar(k); %#ok
if i == 1
Tstar(i) = u(i); %#ok
else
Tstar(i) = Tstar(i-1) + u(i);
end
if Tstar(i) > t
h = {h};
break
end
j = j + 1;
U(j) = rand;
if U(j) <= custom(1,Tstar(i),{h},par)/Lstar(k)
n = n + 1;
h = [h Tstar(i)];
do5 = true;
else
k = k + 1;
Lstar(k) = custom(1,Tstar(i),{h},par);
do5 = false;
end
end
else
h = {[]};
end
And here is the application:
par2.mu = 0.5;
par2.alpha = 0.1;
par2.beta = 0.3;
t = 1000;
h2 = simcustom(t,par2);