MATLAB: Two questions about the code: 1.) Estimating random number with and without rng (‘shuffle’); 2.) storaging results

Question

I want to estimate random numbers with the weibull distribution.

1.) "wblrnd" generates random numbers of my function "custompdf". So do "rng ('shuffle')".

In "results" I can see my results. When I run my code(without changing it), it displays random numbers.

When I I delete the line with rng ('shuffle'), it also display random numbers.

So whats the difference?

2.) Someone helped me to storage my code for a better overview and for flexibilty of "b" and "T" (In case I change them)

Its the line beginning with "results". It works really nice, but I dont really understand the line. Can someone explain what the line is doing? I am really a noob in Matlab.

clear all;
n   = 100;
t0  = 0.5;
b = 1:3;
T = 1:3;
rng ('shuffle')
for v_T= T
    for v_b= b
        data(:,v_b,v_T) = wblrnd(v_b,v_T, [n,1]) + t0;
        start       = [1 0 0];
        custompdf   = @(x,a,b,c) (x>c).*(b/(a-c)).*(((x-c)/(a-c)).^(b-1)).*exp(-((x-c)/(a-c)).^b);
        opt         = statset('MaxIter',1e3,'MaxFunEvals',1e3,'FunValCheck','off');
        params(v_b,1:3,v_T) = mle(data(:,v_b,v_T),'pdf',custompdf,'start',start,'Options',opt,'LowerBound',[0 0 0],'UpperBound',[Inf Inf min(data(:,v_b,v_T))])
        params(v_b,4,v_T)   = v_b;
        params(v_b,5,v_T)   = v_T;
        params(v_b,6,v_T)   = t0;
        params(v_b,7,v_T)   = n;
    end
   results((v_T-1)*length(b)+1:v_T*length(b), 1:size(params, 2)) = params(:,:,v_T);
end

Answer 1

For the first question, when you start MATLAB the "deck" of random numbers (technically it's a stream, but deck fits the metaphor better) is in a known order. When you generate a random number ("pull the top card of the deck") that first number is always the same. [When you use rng default that "stacks the deck" back to this ordering.]

You can think of rng shuffle as shuffling that "deck" to a new order. [Technically it's probably more similar to cutting the deck at a point based on the current time and date but it's a metaphor. It doesn't have to be a 100% accurate representation of reality.]

If the deck had been stacked before, it wouldn't be now. So you'd go from knowing exactly which number you'd generate next to not knowing.

If the deck hadn't be stacked before, it still won't be. So you'd go from not knowing which number is next to still not knowing which is next.