Comparison between Poisson Distribution, Gaussian (Normal) Distribution and Logistic Regression
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Table 3838. Comparison between Poisson Distribution, Gaussian (Normal) Distribution and Logistic Regression.

  Poisson Distribution Gaussian (Normal) Distribution Logistic Regression
Type of Distribution Probability distribution used for count data (discrete data) Probability distribution used for continuous data. A statistical model used for binary classification and estimating probabilities.
Key Assumption Assumes that events occur at a constant rate and are independent of each other. Assumes that data follows a bell-shaped curve, is symmetric, and unimodal. Assumes a linear relationship between the predictor variables and the log-odds of the binary outcome (logit function).
Probability Range The Poisson distribution is defined for non-negative integers (0, 1, 2, 3, ...). The Gaussian distribution is defined over the entire real number line (-∞ to +∞). The outcome variable in logistic regression is binary (0 or 1) and represents the probability of an event occurring.
Typical Use Cases Used for modeling count data, such as the number of customer arrivals at a store, the number of emails received per hour, etc. Used for modeling continuous data, such as heights of individuals, errors in measurements, and many natural phenomena. Used for binary classification tasks, such as spam email detection, disease diagnosis, and credit risk assessment.
Model Function Probability Density Function (PDF): Describes the probability of observing a specific count of events. PDF: Describes the likelihood of observing a specific value within the continuous range. The logistic regression model uses the logistic function (sigmoid function) to transform the linear combination of predictors into probabilities between 0 and 1.
Others Poisson and Gaussian distributions are more commonly associated with different types of data and modeling tasks than logistic regression. Logistic regression is specifically designed for binary classification problems, and it involves the logistic function to model the probabilities of binary outcomes.

 

 

       

        

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