Exponential Family

def. Expoential Family of Distributions is the distributions whose pdfs are in the following form:

$$f_X(x|\theta )=h(x)\cdot \text{exp}[\eta (\theta )T(x)-A(\eta )]$$

Includes:

• Normal Distribution
• Exponential Distribution
• Chi-Squared
• Beta
• Diriochelt
• Bernouilli Distribution
• Poisson Distribution

As well as:

• Binomial Distribution (with fixed number of trials)
• Multinomial Distribution (with fixed number of trials),
• Negative binomial (with fixed number of failures)
• Geometric (Not Hypergeometric!)