Probability distribution. Gallery of Distributions Gallery of Common Distributions Detailed information on a few of the most common distributions is available below. There are a large number of distributions used in statistical applications. It is beyond the scope of this Handbook to discuss more than a few of these. Two excellent sources for additional detailed information on a large array of distributions are Johnson, Kotz, and Balakrishnan and Evans, Hastings, and Peacock. Equations for the probability functions are given for the standard form of the distribution. Formulas exist for defining the functions with location and scale parameters in terms of the standard form of the distribution. The sections on parameter estimation are restricted to the method of moments and maximum likelihood. This is because the least squares and PPCC and probability plot estimation procedures are generic. The maximum likelihood equations are not listed if they involve solving simultaneous equations. This is because these methods require sophisticated computer software to solve. Except where the maximum likelihood estimates are trivial, you should depend on a statistical software program to compute them. References are given for those who are interested. Be aware that different sources may give formulas that are different from those shown here. In some cases, these are simply mathematically equivalent formulations. In other cases, a different parameterization may be used. Continuous Distributions Normal Distribution Uniform Distribution Cauchy Distribution t Distribution F Distribution Chi-Square Distribution Exponential Distribution Weibull Distribution Lognormal Distribution Birnbaum-Saunders (Fatigue Life) Distribution Gamma Distribution Double Exponential Distribution Power Normal Distribution Power Lognormal Distribution Tukey-Lambda Distribution Extreme Value Type I Distribution Beta Distribution Discrete Distributions Binomial Distribution Poisson Distribution

Probability Distributions

Probability Distributions

Probability distributions are a fundamental concept in statistics. They are used both on a theoretical level and a practical level.Some practical uses of probability distributions are: To calculate confidence intervals for parameters and to calculate critical regions for hypothesis tests. For univariate data, it is often useful to determine a reasonable distributional model for the data. Statistical intervals and hypothesis tests are often based on specific distributional assumptions. Before computing an interval or test based on a distributional assumption, we need to verify that the assumption is justified for the given data set. In this case, the distribution does not need to be the best-fitting distribution for the data, but an adequate enough model so that the statistical technique yields valid conclusions. Simulation studies with random numbers generated from using a specific probability distribution are often needed. . Gallery of Distributions Gallery of Common Distributions Detailed information on a few of the most common distributions is available below. There are a large number of distributions used in statistical applications. It is beyond the scope of this Handbook to discuss more than a few of these. Two excellent sources for additional detailed information on a large array of distributions areJohnson, Kotz, and Balakrishnan and Evans, Hastings, and Peacock. Equations for the probability functions are given for thestandard form of the distribution. Formulas exist for defining the functions with location and scale parameters in terms of the standard form of the distribution.The sections on parameter estimation are restricted to the method of moments and maximum likelihood. This is because the least squares and PPCC and probability plot estimation procedures are generic. The maximum likelihood equations are not listed if they involve solving simultaneous equations. This is because these methods require sophisticated computer software to solve. Except where the maximum likelihood estimates are trivial, you should depend on a statistical software program to compute them. References are given for those who are interested. Be aware that different sources may give formulas that are different from those shown here. In some cases, these are simply mathematically equivalent formulations. In other cases, a different parameterization may be used. Continuous Distributions Normal Distribution Uniform Distribution Cauchy Distribution t Distribution F Distribution Chi-Square Distribution Exponential Distribution Weibull Distribution Lognormal Distribution Birnbaum-Saunders (Fatigue Life) Distribution Gamma Distribution Double Exponential Distribution Power Normal Distribution Power Lognormal Distribution Tukey-Lambda Distribution Extreme Value Type I Distribution Beta Distribution Discrete Distributions Binomial Distribution Poisson Distribution