### TABLE 1 PARAMETERS FOR EXPONENTIAL FAMILY DISTRIBUTIONS

### Table 1. Canonical representation of some exponential

2005

Cited by 5

### Table 2: Canonical decompositions of usual exponential families. 12

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

2001

Cited by 47

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

2001

Cited by 47

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

2001

Cited by 47

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

2001

Cited by 47

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

2001

Cited by 47

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

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