PoissonNäherungen

PoissonNäherungen refers to approximations that utilize the Poisson distribution. The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. Poisson Näherungen are often employed when a binomial distribution has a large number of trials and a small probability of success. In such cases, the Poisson distribution can serve as a good approximation to the binomial distribution. This approximation is particularly useful when calculating probabilities for rare events. Another common application involves approximating a normal distribution with a Poisson distribution, although this is less frequently encountered than the binomial approximation. The key condition for the Poisson approximation to the binomial distribution is that the expected value, np, remains constant as n approaches infinity and p approaches zero. The parameter lambda (λ) of the Poisson distribution in this approximation is equal to the expected value of the binomial distribution, which is np. This simplification allows for easier calculation and interpretation of probabilities in scenarios where direct binomial calculation might be computationally intensive.