Poisson Distribution
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.
Poisson Distribution
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. It is named after the French mathematician Siméon-Denis Poisson. The Poisson distribution is a discrete function, meaning the variable can only take specific values from a (potentially infinite) list. In other words, the variable cannot take all values within any continuous range. For the Poisson distribution, the variable can only take integer values (0, 1, 2, 3, etc.), not fractions or decimals.
Origin
The Poisson distribution was first introduced by the French mathematician Siméon-Denis Poisson in 1837. Poisson discovered the characteristics of this distribution while studying the frequency of random events and applied it to various fields such as insurance, physics, and biostatistics.
Categories and Characteristics
The main characteristics of the Poisson distribution include:
- Discreteness: The Poisson distribution is a discrete distribution, and the variable can only take non-negative integer values.
- Parameter λ (lambda): The Poisson distribution is determined by a single parameter λ, which represents the average number of events occurring within a given time interval.
- Independence: The occurrence of events is independent, meaning the occurrence of one event does not affect the occurrence of another.
- Constant Rate: The rate at which events occur is constant and does not change over time.
Examples
Example 1: An emergency room in a city receives an average of 5 patients per hour. Assuming the arrival of patients follows a Poisson distribution, the probability of receiving 8 patients in a particular hour can be calculated using the Poisson distribution formula.
Example 2: A website's server receives an average of 3 requests per minute. Assuming the arrival of requests follows a Poisson distribution, the probability of receiving 5 requests in a particular minute can be calculated using the Poisson distribution formula.
Common Questions
Q1: What is the difference between the Poisson distribution and the normal distribution?
A1: The Poisson distribution is a discrete distribution suitable for count data, while the normal distribution is a continuous distribution suitable for measurement data.
Q2: How is the parameter λ of the Poisson distribution determined?
A2: The parameter λ is usually estimated from the average number of occurrences in historical data.
