Computes the complementary log-log transformation, including its inverse.
Syntax
CLOGLOG(X, Return_type)
- X
- the real number for which we compute the transformation.
- Return_type
- is a number that determines the type of return value: 1 (or missing)= C-Log-Log , 2= Inverse C-Log-Log.
RETURN_TYPE NUMBER RETURNED 1 or omitted C-Log-Log Transform 2 Inverse of C-LOg-Log transform
Remarks
- The complementary log-log link function is commonly used for parameters that lie in the unit interval.
- The Complementary log-log transformation is defined as follows:
$$y=\textit{CLogLog}(x)=\ln\left( -\ln \left ( 1-x \right) \right) $$ And
$$x=\textit{CLogLog}^{-1}(y)=1 - e^{-e^{y}} $$
Where:
- $x_{t}$ is the value of the input time series at time $t$
- $y_{t}$ is the transformed complementary log-log value at time $t$
- $\textit{ClogLog}^{-1}(y)$ is the inverse complementary log-log function
- $\left(x_t +\alpha \right) \gt 0$ for all t values
- The BOXCOX function accepts a single value or an array of values for X.
- The shift parameter must be large enough to make all the values of X positive.
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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