Latin Hypercube sampling from distrete, non-uniform distribution
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I have a series of independent events that are assumed to indiviudally have poisson distributions.
I first calculate the number of events in an annual period by using the compound poisson first principles.
Then I need to sample from the data to see which events occur (the number of events ranges for any given year range from 0 to 5). USing brute force monte carlo, I get convergence in the tail characteristics but only after extreme numbers of sampling.
I would like to reduce the number of samples while preserving the representative distributions evn when sampling in years with mroe than 1 event. For loops do not preserve the full distributions outside of the loop.
I do not see any natural latin hyper cube functionality within the statsitics toolbox that uses discrete distributions and perserves distributions for multiple event years.
Thansk in advance.
I can't think of any good way to use the latin hypercube feature here. You can apply poissinv to a distribution inside the unit cube, but I suspect that will not help.
I don't completely understand your scenario. If your total event number is the sum of independent Poisson values, then the sum itself is also Poisson. Furthermore, I believe the individual values, conditional on the sum, have a multinomial distribution. Can you make use of that?
This is probably not what you want, but if you explain further why it's not what you want, maybe we can come closer to a solution. To sample intervals of unequal length or probability:
edges = [0 .4 .5 .8 1]';
[~,b] = histc(rand(1000,1),edges);
v = mnrnd(1,diff(edges),1000);
b = v*(1:4)';
To sample within a specified range of probabilities:
d = diff(edges);