Probit

In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution, which is commonly denoted as N(0,1). Mathematically, it is the inverse of the cumulative distribution function of the standard normal distribution, which is denoted as ${\displaystyle \Phi (z)}$, so the probit is denoted as ${\displaystyle \Phi ^{-1}(p)}$. It has applications in exploratory statistical graphics and specialized regression modeling of binary response variables.

Largely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics. If we consider the familiar fact that the standard normal distribution places 95% of probability between −1.96 and 1.96, and is symmetric around zero, it follows that

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