Computes the probit transformation, including its inverse.
Syntax
PROBIT(X, Return_type)
- X
- the real number for which we compute the transformation. X must be between zero and one (exclusive).
- Return_type
- is a number that determines the type of return value: 1 (or missing)= Probit , 2= Inverse Probit.
RETURN_TYPE NUMBER RETURNED 1 or omitted Probit Transform 2 Inverse of Probit transform
Remarks
- The probit link function is commonly used for parameters that lie in the unit interval.
- Numerical values of X close to 0 or 1 or out of range result in #VALUE! or #N/A.
- 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
- The Probit function accepts a single value or an array of values for X.
Examples
Example 1:
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Files Examples
Related Links
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
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