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Relationships among some of univariate probability distributions are illustrated with connected lines. dashed lines means approximate relationship. more info: [1] Relationships between univariate probability distributions in ProbOnto. [2] In probability theory and statistics, there are several relationships among probability distributions ...
The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa. The first cumulant is the mean , the second cumulant is the variance , and the third cumulant is the same as the third central moment .
ProbOnto is a knowledge base and ontology of probability distributions. [1] [2] ProbOnto 2.5 (released on January 16, 2017) contains over 150 uni- and multivariate distributions and alternative parameterizations, more than 220 relationships and re-parameterization formulas, supporting also the encoding of empirical and univariate mixture distributions.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y , the distribution of the random variable Z that is formed as the product Z = X Y {\displaystyle Z=XY} is a product distribution .
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.