2010•Unpublished venueRequires access
Exponential Family
Catherine Forbes, Merran Evans, Nicholas Anthony John Hastings, Brian Peacock
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Abstract
Exponential family include the univariate Bernoulli, binomial, Poisson, geometric, gamma, normal, inverse Gaussian, logarithmic, Rayleigh, and von Mises distributions. Multivariate distributions include the multinomial, multivariate normal, Dirichlet, and Wishart. The natural exponential family has B(x) = x, with A(θ) the natural or canonical parameter. The shared important properties of exponential families enable estimation by likelihood methods, using computer programs such as GenStat, R, or Stata. This chapter discusses generalized exponential distributions such as generalized Student’s t distribution, generalized exponential normal distribution, generalized lognormal distribution, and variate relationships. Controlled Vocabulary Terms control variate; exponential family; log-normal distribution; normal distribution; Student’s t-distribution