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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.
Using the distribution semantics, a probability distribution is defined over the two-valued well-founded models of the atoms in the program. The probability of a model is defined as P ( M ) = ∏ l ∈ M P ( l ) {\displaystyle P(M)=\prod _{l\in M}P(l)} where the product runs over all the literals in the model M {\displaystyle M} .
When =, the Von Mises–Fisher distribution, (,) on simplifies to the uniform distribution on . The density is constant with value C p ( 0 ) {\displaystyle C_{p}(0)} . Pseudo-random samples can be generated by generating samples in R p {\displaystyle \mathbb {R} ^{p}} from the standard multivariate normal distribution, followed by normalization ...
The obvious problem which occurs when the actual distribution is not in fact a second-order dependency tree can still in some cases be addressed by fusing or aggregating together densely connected subsets of variables to obtain a "large-node" Chow–Liu tree (Huang, King & Lyu 2002), or by extending the idea of greedy maximum branch weight selection to non-tree (multiple parent) structures ...
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.
The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.
The distribution is called "folded" because probability mass to the left of x = 0 is folded over by taking the absolute value. In the physics of heat conduction, the folded normal distribution is a fundamental solution of the heat equation on the half space; it corresponds to having a perfect insulator on a hyperplane through the origin.
The parameters governing the Pitman–Yor process are: 0 ≤ d < 1 a discount parameter, a strength parameter θ > −d and a base distribution G 0 over a probability space X. When d = 0, it becomes the Dirichlet process .