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A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...
In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are the Karger–Stein algorithm [ 1 ] and the Monte Carlo algorithm for minimum feedback arc set .
The number of claims N is a random variable, which is said to have a "claim number distribution", and which can take values 0, 1, 2, .... etc..For the "Panjer recursion", the probability distribution of N has to be a member of the Panjer class, otherwise known as the (a,b,0) class of distributions.
the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats) the (pseudo-random) number generator produces values that pass tests for randomness; there are enough samples to ensure accurate results; the proper sampling technique is used; the algorithm used is valid for what is being modeled
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Then, there might be a tie. Following the weight update rule in weighted majority algorithm, the predictions made by the algorithm would be randomized. The algorithm calculates the probabilities of experts predicting positive or negatives, and then makes a random decision based on the computed fraction: [further explanation needed] predict
A Monte Carlo algorithm is a randomized algorithm which is likely to be correct. Problems in the class BPP have Monte Carlo algorithms with polynomial bounded running time. This is compared to a Las Vegas algorithm which is a randomized algorithm which either outputs the correct answer, or outputs "fail" with low probability.
A simple randomized algorithm developed by Manindra Agrawal and Somenath Biswas can determine probabilistically whether is prime and uses polynomial identity testing to do so. They propose that all prime numbers n (and only prime numbers) satisfy the following polynomial identity: