Chi-Squared Distribution
By M. Manser, S. Swamy, James Blanchard Econ. 2010
1 What is it? The Chi-Squared distribution is a one parameter distribution with density function: f (x) = x k/2−1 e −x/2 Γ(k/2)2 k/2 where k is the parameter, x is a random variable with x ∈ [0, ∞), and Γ(x) is the Gamma function, defined as Γ(x) = (x − 1)! for integers and Γ(x) = ∞ o t x−1 e −t dt when x is not an integer. A few examples with the parameter value, k, varying. In this example k takes values of 1,2,3,4,5.
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Citations in the corpus
- A Kernel Test for Three-Variable Interactions (2013, methodology): “An interaction measure [21, 22] associated to a multidimensional probability distribution P of a random vector (X1, .”
- Information theoretic measures for clusterings comparison: is a correction for chance necessary? (2009, background): “A common model for randomness is the “permutation model” (Lancaster, 1969, p. 214), in which clusterings are generated randomly subject to having a fixed number of clusters and points in each clusters.”
- An introduction to multivariate Krawtchouk polynomials and their applications (2013, methodology): “These matrices were used by Lancaster and Irwin to decompose the usual chi-square test for goodness of fit to a multinomial model into d orthogonal pieces. See Lancaster (1969). Saltzman (2010) has observed that the u(l) diagonalize a natural Markov chain.”
- Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance (2010, background): “Such a common model is the " permutation model " (Lancaster, 1969, p. 214), in which clusterings are generated randomly subject to having a fixed number of clusters and points in each clusters.”
- Gibbs sampling, exponential families and orthogonal polynomials (2008, background): “The part of interest here begins with the work of Lancaster, nicely summarized in his book [72].”