The best replacement for bernoulli is binomial.

The best alternatives to bernoulli are rated as following:
★★★★★  binomial
★★★★★  newton
★★★  venturi
★★  coanda
★★  poisson
★  venturi effect
★  magnus effect
  binomial distribution
  bernoulli
  lightning mcqueen

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Speaking about bernoulli, one probably shouldn't forget about bayes.

Other search terms related to bernoulli and their ratings are:
★★★★★ bayes
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