TATITIC CALCULATOR
Poisson Distribution
A precise tool.
What is the Poisson Distribution & How does it work?
The Poisson distribution models the probability of a given number of events occurring in a fixed interval of time or space when these events happen with a known constant mean rate and independently of the time since the last event.
It is widely used in fields such as telecommunications, traffic engineering, and biology to predict rare event counts like call arrivals, accidents, or mutations.
P(X = k) = \frac{\lambda^{k} e^{-\lambda}}{k!}
\lambda = average rate (mean number of events), k = observed count of events
When the mean number of events is large, the Poisson distribution approximates the normal distribution, while for very small means it provides a more accurate discrete model than the binomial.
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Frequently Asked Questions
What is the Poisson distribution used for?
The Poisson distribution is used to model the number of times an event occurs in a fixed interval of time or space, such as call arrivals, accidents, or mutations.
How do I calculate the mean rate (Ξ») for the Poisson distribution?
The mean rate (Ξ») is calculated by dividing the total number of events by the total amount of time or space over which they occurred.
Can the Poisson distribution be used for continuous data?
No, the Poisson distribution is specifically designed for discrete data where the events are counted.
What is the formula for the Poisson distribution?
The formula for the Poisson distribution is P(X = k) = (Ξ»^k * e^(-Ξ»)) / k!, where Ξ» is the average rate and k is the observed number of events.
When should I use the Poisson distribution instead of the binomial distribution?
Use the Poisson distribution when the number of trials (n) is large and the probability of success (p) is small, such that np is a constant Ξ». The binomial distribution is used for a fixed number of trials with a binary outcome.
What does e represent in the Poisson formula?
In the Poisson formula, e represents the base of the natural logarithm, approximately equal to 2.71828.
Can the Poisson distribution be used for negative values of Ξ»?
No, the mean rate (Ξ») must be a non-negative real number in the Poisson distribution.
Results are for informational purposes only and do not constitute professional advice.