MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 16: Indian Institute Of Technology Kanpur, Exponential Family, Poisson Regression

• School: Indian Institute of Technology - IIT Kanpur
• Department: Mathematics
• Course: MTH-416, REGRESSION ANALYSIS
• Professor: All

Document Summary

The usual linear regression model assumes a normal distribution of study variables whereas nonlinear logistic and poison regressions are based on bernoulli and poisson distributions, respectively of study variables. Similar to as in logistic and poisson regressions, the study variable can follow different probability distributions like exponential, gamma, inverse normal etc. One such family of distribution is described by the exponential family of distributions. The generalized linear model is based on this distribution and unifies linear and nonlinear regression models. It assumes that the distribution of the study variable is a member of the exponential family of distribution. A random variable x belongs to the exponential family with a single parameter has a probability density function exp ( a x b d x f x c d x. ), ( ), ( ) and ( are all known function. the distribution is said to be in canonical form. The function where ( )b is called the natural.