Question

Cauchy distribution is not a exponential family

Answer 1

THIS IS NOT CONSTANT AS A FUNCTION OF SO THE CAUCHY FAMILY IS NOT AN EXPONENTIAL FAMILY. ONE-PARAMETER EXPONENTIAL FAMILIES HAVE A NATURAL ONE-DIMENSIONAL SUFFICIENT STATISTIC REGARDLESS OF THE SAMPLE SIZE. A K-PARAMETER EXPONENTIAL FAMILY HAS A K-DIMENSIONAL SUFFICIENT STATISTIC REGARDLESS OF THE SAMPLE SIZE.

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