In credit scoring, the logit model theory is described as assuming what about the probability of default?

• A. It assumes that the probability of default is logically distributed.
• B. It assumes the probability of default follows a logistic distribution.
• C. It assumes the probability of default has a cumulative normal distribution.
• D. It assumes the probability of default is independent of input factors.

Answer: (A)

In a logit model for credit scoring, the probability of default is connected to the input factors through a logistic function. This means the log-odds of default are modeled as a linear combination of the predictors: log(p/(1-p)) = β0 + β1x1 + …, so the probability itself is p = 1 / (1 + exp(-(β0 + β1x1 + …))). This setup implies a logistic distribution for the latent error term in the underlying propensity to default, which leads to the logistic shape when converting the linear predictor to a probability. In short, the model assumes the logistic relationship between the predictors and the default probability, not a normal (probit) or other distribution, and the probability is clearly tied to the input factors rather than being independent of them.