Probitfunktiolle

Probitfunktiolle, often referred to as the probit function, is a cumulative distribution function (CDF) derived from the standard normal distribution. It is used in statistical modeling, particularly in probit regression, to model the probability of a binary outcome. The probit function maps a variable, often a linear combination of predictors, to a probability between 0 and 1. Mathematically, it is represented as $\Phi(z) = \int_{-\infty}^{z} \frac{1}{\sqrt{2\pi}} e^{-\frac{t^2}{2}} dt$, where $z$ is the input variable and $\Phi$ denotes the standard normal CDF. This function is the inverse of the quantile function of the standard normal distribution. In probit regression, it assumes that the underlying latent variable follows a normal distribution. When the latent variable exceeds a certain threshold, the observed binary outcome is predicted to occur. The probit function is a common alternative to the logistic function (logit) in binary classification problems, though it typically yields very similar results in practice. The interpretation of coefficients in probit models relates to changes in the probability of the outcome as predictors change.