In a standard logistic regression analysis, which distribution is typically used?

In standard logistic regression analysis, the binomial distribution is used because logistic regression is designed to model binary outcome variables—those that take on two possible values, such as success/failure, yes/no, or 1/0. The key characteristic of a binomial distribution is that it describes the number of successes in a fixed number of independent Bernoulli trials, which fits perfectly with the binary nature of the outcomes in logistic regression.

The logistic function itself models the probability that the dependent variable equals one of the two outcomes, and it is derived based on the premise that the log-odds of the probability of success follows a linear relationship with the independent variables. This connection to the binomial distribution allows practitioners to estimate the probabilities of different outcomes based on the predictor variables.

In contrast, the normal distribution is more applicable to continuous outcomes, while the Poisson distribution is typically used for count data, and the exponential distribution pertains to time until an event occurs. Each of these distributions serves different types of data and statistical modeling scenarios, highlighting why the binomial distribution is the appropriate choice for logistic regression.