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cfi
2024 Jan 23
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Quantiles of sums of independent discrete random variables
Greetings,
I have the following?
Problem:
Given k (=10) discrete independent random variables X_i with n_i (= 5 to 20) values each,compute quantiles of the distribution of the sum X = X_1+...+X_k.
Here X has n=n_1 x n_2 ... n_k distinct values which is too large to list them all together with
their probabilities.
I tried several approaches:
(A) Convolution:
each X_j is approximated with