18. Exponential Family

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch18

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Exponential Family, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch18

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242

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Keywords:

  • exponential family;
  • generalized exponential normal distribution;
  • generalized lognormal distribution;
  • generalized Student’s t distribution;
  • parameter estimation;
  • variate

Summary

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