Random draws from conditional multinomial distribution

I have to simulate data for 100 agents over 10,000 time periods for a variable, x. The initial value of x at time 0 for all agents is 0. The distribution of is a multinomial distribution, conditional on the past period's value, . Basically, can remain unchanged with probability 0.2, increase by 2571 with probability 0.5, increase by 2571*2 with probability 0.2, and increase by 2571*3 with probability 0.1, at any period. can never be lower than . How do I generate random values for this distribution?

I have tried:

 x = mnrnd()
 

command, but I can't fit it to these specifications. Any help would be greatly appreciated!

Answer 1

[Alan Stevens]

Something like

u = rand(1)
if u<0.2
    d = 0;
elseif u<0.7
    d = 2571;
elseif u<0.9
    d = 2571^2;
else 
    d = 2571^3;
end
x(t) = x(t-1) + d;

(the last line assumes t is an integer).

[Laura Freitas]

That works, but is this representative of a multinomial distribution? Also, would this not entail the "random" values for each agent end up being all the same? I am asking as a beginner.

[Alan Stevens]

If you turn that code into a function you can call it for each 'agent'.

I don't know what you mean by ' ..representative of a multinomial distribution'. You have specified the way the increases are applied with their corresponding probabilities. I've merely suggested a way of implementing that.

[Laura Freitas]

Can you please explain how I would turn the code into a function?

[Alan Stevens]

function xnew = fn(x,t)
u = rand;
if u<0.2
    d = 0;
elseif u<0.7
    d = 2571;
elseif u<0.9
    d = 2571^2;
else 
    d = 2571^3;
end
x(t) = x(t-1) + d;
end

Note that functions go at the end of a script.

[Laura Freitas]

It worked! Thanks!