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R implementation of a Multinominal Problem: Probability of n-times head in k throws with varying probabilities per throw

im struggling with a potential easy to solve Problem. I have a dataset with 100k series of coin throws with varying k (throws). For each series I want to compute the the probability for each discrete ...
David D's user avatar
3 votes
1 answer
367 views

How to show linear combination of independent, but non-identically distributed Bernoulli's is asymptotically normal?

Summary I am curious about whether there exists theoretical justification to say a linear combination of a sufficiently large number of independent (but not identically distributed) Bernoulli random ...
user365119's user avatar
0 votes
0 answers
159 views

Hypothesis testing two weighted Poisson Binomial Distributions with different lengths

I have two groups of people: each group is made by subgroups of people coming from census areas of which I know the probability of being male vs female. I can calculate the distribution: is a Poisson ...
Alex Darsonik's user avatar
1 vote
0 answers
88 views

Which kind of diagnostic plots for count data? [duplicate]

I know that for an lm model is enough to run plot(model_lm) to get diagnostic plots. I am dealing with high-dimensional count ...
Mary's user avatar
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43 votes
9 answers
15k views

How can I efficiently model the sum of Bernoulli random variables?

I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where $\...
David B's user avatar
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