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TABLE 1 PARAMETERS FOR EXPONENTIAL FAMILY DISTRIBUTIONS

in A SYSTEMATIC RELATIONSHIP BETWEEN MINIMUM BIAS AND GENERALIZED LINEAR MODELS
by Stephen Mildenhall

Table 2: Canonical decompositions of usual exponential families. 12

in unknown title
by unknown authors 709
"... In PAGE 11: ... Regular exponential families include many famous distribution laws such as Bernoulli (multinomial), Normal (univariate, multivariate and recti ed), Pois- son, Laplacian, negative binomial, Rayleigh, Wishart, Dirichlet, and Gamma distributions. Table2 summarizes the various relevant parts of the canonical decompositions of some of these usual statistical distributions. Observe that the product of any two distributions of the same exponential family is another exponential family distribution that may not have any- more a nice parametric form (except for products of normal distribution pdfs that yield again normal distribution pdfs).... In PAGE 13: ... Before proving the theorem, we note that rF ( ) = Z x f(x) expfh ; f(x)i F ( ) + C(x)gdx : (8) The coordinates of def= rF ( ) = [R x f(x)p(xj )dx] = E (f(x)) are called the expecta- tion parameters. As an example, consider the univariate normal distribution N ( ; ) with su cient statistics [x x2]T (see Table2 ). The expectation parameters are = rF ( ) = [ 2 + 2]T , where = R x x p(xj )dx and 2 + 2 = R x x2p(xj )dx.... ..."

Table 1: Various functions of interest for three members of the exponential family

in A Generalization of Principal Component Analysis to the Exponential Family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapire 2001
Cited by 47

Table 1: Various functions of interest for three members of the exponential family

in A Generalization of Principal Component Analysis to the Exponential Family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapire 2001
Cited by 47

Table 1: Various functions of interest for three members of the exponential family

in A Generalization of Principal Component Analysis to the Exponential Family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapire 2001
Cited by 47

Table 1: Various functions of interest for three members of the exponential family

in A generalization of principal component analysis to the exponential family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapire 2001
Cited by 47

Table 1: Various functions of interest for three members of the exponential family

in A Generalization of Principal Component Analysis to the Exponential Family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapire 2001
Cited by 47

Table 1. Deflnition of A and K in natural form for some exponential families.

in Bhattacharyya and Expected Likelihood Kernels
by Tony Jebara, Risi Kondor 2003
"... In PAGE 5: ... Often, T (x) is just x. Many familiar distributions, such as the Normal, Bernoulli, Multinomial, Poisson and Gamma distributions can be written in this form ( Table1 ). Note that A and K are related through the Laplace transform K( ) = log Z exp(A(x) + TT (x)) dx since p(xj ) is normalized.... ..."
Cited by 10

Table 1: Length of flat portionof the FR of exponentiated Weibul l family

in On the Change Points of Mean Residual Life and Failure Rate for Some Extended Weibull Distributions
by Y. Tang, M. Xie, T.N. Goh

Table 1: Various functions of interest for three members of the exponential family

in A Generalization of Principal ComponentAnalysis to the Exponential Family
by Michael Collins, Sanjoy Dasgupta, Robert E. Schapireat, T Labs
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