PROBIT - Probit Transform

1. The probit link function is commonly used for parameters that lie in the unit interval.
2. Numerical values of X close to 0 or 1 or out of range result in #VALUE! or #N/A.
3. The probit function is defined as the inverse cumulative distribution function (CDF):
   $$ y=\textit{Probit}(x)=\Phi^{-1}(x)$$
   And
   $$ x=\textit{probit}^{-1}(y)=\Phi(y)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{y}e^{\frac{-Z^2}{2}}dz $$
   Where:
   
   • $x_{t}$ is the value of the input time series at time $t$
   • $y_{t}$ is the transformed probit value at time $t$
   • $\textit{probit}^{-1}(y)$ is the inverse probit function
4. The Probit function accepts a single value or an array of values for X.

Example 1:

Files Examples

Related Links

• Wikipedia - Probit transform

References

• John H. Aldrich, Forrest D. Nelson; Linear Probability, Logit, and Probit Models; SAGE Publications, Inc; 1st Edition(Nov 01, 1984), ISBN: 0803921330
• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740