PLANETCALC Online calculators

Login
ProfessionalStatistics

Poisson Distribution. Probability density function, cumulative distribution function, mean and variance

This calculator calculates poisson distribution pdf, cdf, mean and variance for given parameters

This page exists due to the efforts of the following people:

Timur

Timur

Created: 2018-02-09 08:16:17, Last updated: 2021-03-06 09:47:15
Creative Commons Attribution/Share-Alike License 3.0 (Unported)

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/7708/. Also, please do not modify any references to the original work (if any) contained in this content.

In probability theory and statistics, the Poisson distribution, named after French mathematician Siméon Denis Poisson, 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 rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area, or volume. Wikipedia

Probability density function of the poisson distribution is
f(k)=\frac{e^{-\lambda}\lambda^x}{x!},
where lambda is a parameter 0 < \lambda < \infinity which equals the average number of events per interval. It is also called the rate parameter.

For instance, on a particular river, overflow floods occur once every 100 years on average. If we assume the Poisson model is appropriate, we can calculate the probability of k = 0, 1, ... overflow floods in a 100-year interval using a Poisson distribution with lambda equals 1.

Cumulative distribution function of the poisson distribution is
F(k)=e^{-\lambda }\sum _{i=0}^{\lfloor k\rfloor }{\frac {\lambda ^{i}}{i!}}\ ,
where \lfloor k\rfloor is the floor function

Mean or expected value for the poisson distribution is
\mu_x=\lambda

Variance is
\sigma^{2}_{x}=\lambda

The calculator below calculates the mean and variance of Poisson distribution and plots probability density function and cumulative distribution function for given parameters lambda and n - number of points to plot on the chart.

PLANETCALC, Poisson Distribution. Probability density function, cumulative distribution function, mean and variance

Poisson Distribution. Probability density function, cumulative distribution function, mean and variance

Digits after the decimal point: 2
Mean
 
Variance
 
Probability density function
The file is very large. Browser slowdown may occur during loading and creation.
Cumulative distribution function
The file is very large. Browser slowdown may occur during loading and creation.

URL copied to clipboard

Similar calculators

 CDF cumulative distribution function Distribution hypergeometric distribution Mean PDF probability probability density function Statistics Variance
PLANETCALC, Poisson Distribution. Probability density function, cumulative distribution function, mean and variance
Timur2021-03-06 09:47:15

Comments