Inferential statistics is the science of learning from data. Data are typically viewed as random variables or vectors, but in contrast to our discussion of probability, distributions for these variables are generally unknown. In applications, it is often reasonable to assume that distributions come from a suitable class of distributions. In this chapter we introduce classes of distributions called exponential families. Examples include the binomial, Poisson, normal, exponential, geometric, and other distributions in regular use. From a theoretical perspective, exponential families are quite regular. In addition, moments for these distributions can often be computed easily using the differential identities in Section 2.4.
KeywordsLebesgue Measure Success Probability Independent Random Variable Unbiased Estimator Exponential Family
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