What is Poisson Distribution?
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In statistics, a Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period. In other words, it is a count distribution. Poisson distributions are often used to understand independent events that occur at a constant rate within a given interval of time. It was named after French mathematician Siméon Denis Poisson.The Poisson distribution is a discrete function, meaning that the variable can only take specific values in a (potentially infinite) list. Put differently, the variable cannot take all values in any continuous range. For the Poisson distribution, the variable can only take whole number values (0, 1, 2, 3, etc.), with no fractions or decimals.
Definition
In statistics, the Poisson distribution is a probability distribution used to represent the number of events occurring within a fixed interval of time. In other words, it is a count distribution. The Poisson distribution is often used to understand independent events occurring at a constant rate within a given time interval.
Origin
The Poisson distribution is named after the French mathematician Siméon Denis Poisson, who made significant contributions to probability theory in the early 19th century. The concept of the Poisson distribution was initially used to describe the frequency of rare events, such as the number of calls received by a telephone switchboard or the occurrence of accidents.
Categories and Features
The Poisson distribution is a discrete probability distribution, meaning the variable can only take integer values (such as 0, 1, 2, 3, etc.) and not fractions or decimals. Its main feature is that the average rate of occurrence (λ) is known, and events occur independently. The probability mass function of the Poisson distribution is P(X=k) = (λ^k * e^(-λ)) / k!, where k is the number of occurrences, and e is the base of the natural logarithm.
Case Studies
A typical case is a telephone company using the Poisson distribution to predict the number of calls received in a specific time period. Suppose a company receives an average of 5 calls per hour; the Poisson distribution can be used to calculate the probability of receiving 3 calls in one hour. Another case is a hospital using the Poisson distribution to predict the number of patients arriving at the emergency room in an hour to allocate resources efficiently.
Common Issues
Common issues investors face when applying the Poisson distribution include misusing it to describe non-independent events or situations where the event rate is not constant. Additionally, the Poisson distribution is not suitable for describing very high-frequency events, as it may closely resemble the normal distribution in such cases.
