Bernoulli Distribution  Python and Machine Learning for Integrated Circuits   An Online Book  

Python and Machine Learning for Integrated Circuits http://www.globalsino.com/ICs/  


Chapter/Index: Introduction  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  Appendix  
================================================================================= The Bernoulli distribution is a fundamental probability distribution in statistics and probability theory. It models a random experiment with two possible outcomes: success (usually denoted as 1) and failure (usually denoted as 0). The distribution is named after Swiss mathematician Jacob Bernoulli (refer to page3887). The Bernoulli distribution is characterized by a single parameter, which is the probability of success, often denoted as "p." The probability mass function (PMF) of the Bernoulli distribution is given by:  [3865a] Where:
Based on Equation 3865a, we can have,  [3865b]  [3865c] Then, comparing with the Exponential Family equation below:  [3865d] we have: h(x) = 1 θ = log(p/(1p)) x = T(x) A(θ) = log(1p) = log(11/(1+exp(θ))) The probability distribution of the dependent variable in logistic regression follows: 1) A Bernoulli distribution for binary logistic regression. 2) A categorical distribution for multinomial logistic regression. ============================================


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