Which modeling approach maps input factors to a default probability via a cumulative normal distribution?

• A. Linear Probability Model
• B. Logit Model
• C. Probit Model
• D. Neural Network

Answer: (C)

The probit model uses the standard normal cumulative distribution function to map a linear combination of input factors to a probability. In this approach, you think of an underlying latent score that is normally distributed; you blend the inputs to form a z-score, then apply the normal CDF to convert that score into a probability. This produces probabilities strictly between 0 and 1 and yields the characteristic S-shaped relationship between the predictors and the probability of default.

Compared to the linear probability model, which applies the linear predictor directly and can give out-of-range values, and the logit model, which uses the logistic function, the probit specifically relies on the cumulative normal distribution. Neural networks can approximate many mappings, but they don't inherently perform this specific normal-CDF transformation.