Which probability distributions are commonly used besides the normal distribution?
Swiss commemorative stamp of mathematician Jakob Bernoulli, issued 1994, displaying the formula and the graph for the law of large numbers, first proved by Bernoulli in 1713.
Beyond the normal distribution, statisticians utilize a variety of discrete and continuous probability distributions to model different types of data and processes.
Discrete Distributions
These distributions model outcomes that occur in countable steps:
* Binomial distribution: Models the number of successes in a fixed number of independent trials, each with a constant probability of success.12
* Poisson distribution: Characterizes the number of events occurring within a fixed interval of time or space, particularly when those events have a low probability of occurrence.2
* Geometric distribution: Models the number of trials needed to achieve the first success in a series of independent Bernoulli trials.34
* Hypergeometric distribution: Describes the probability of successes in a sequence of draws from a finite population without replacement.3
* Negative binomial distribution: Used to model the number of trials required to achieve a specified number of successes.3
Continuous Distributions
These distributions model data that can take on any value within a range:
* Uniform distribution: A distribution where every outcome within a specified range is equally likely.35
* Exponential distribution: Models the time between independent events occurring at a constant average rate.4
* Gamma distribution: Often used to model the time until a specific number of events occurs.34
* Chi-square, Beta, F, and t distributions: These are frequently employed in inferential statistics, such as hypothesis testing, particularly when dealing with unknown parameters or sample means.36