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Continuous Distributions

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Uniform distribution (continuous)
Continuous distribution such that intervals of the same length on the distribution's support are equally probable.
Normal distribution
Most prominent probability distribution arising from the central limit theorem. The density is the bell curve.
Von Mises distribution
Close approximation of the circular analogue of the normal distribution, most commonly used distribution in directional statistics.
Exponential distribution
Describes the time between consecutive rare random events in a process with no memory.
Weibull distribution
Used to model the lifetime of technical devices and the particle size distribution of grinding or crushing operations.
Cauchy-Lorentz distribution
Describes resonance and shape of spectral lines, among others. Example of a "pathological" distribution with undefined mean and variance.
Student's t-distribution
Used in hypothesis testing to compare the means of two normally distributed populations with unknown standard deviation.
Chi-squared distribution
Sum of the squares of k independent standard normal random variables, frequently used for hypothesis testing and construction of confidence intervals, among others.
F-distribution (Fisher-Snedecor)
Ratio of two normalized chi-squared random variables, frequently used as null distribution of a test statistic, most notably in the analysis of variance.
Erlang distribution
Generalization of the exponential distribution used to model waiting times in queueing systems.
Gamma distribution
Generalization of the chi-squared and Erlang distributions with similar applications.
Beta distribution
Applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines.
Pareto distribution
Power law probability distribution that coincides with social, scientific, geophysical, actuarial, and many other types of observable phenomena.
Laplace distribution
Governs the difference between two i.i.d. exponential random variables, used in Brownian motion.
Non-central t-distribution
Usually used to compute the power of a t-test.