
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 bellshaped curve, is symmetric, and unimodal. 
Assumes a linear relationship between the predictor variables and the logodds of the binary outcome (logit function). 
Probability Range 
The Poisson distribution is defined for nonnegative 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. 