Computes the complementary loglog transformation, including its inverse.
Syntax
CLOGLOG(X, Lo, Hi, Return)
 X
 is the real value(s) for which we compute the transformation: a single value or a onedimensional array of cells (e.g., rows or columns)).
 Lo
 is the xdomain lower limit. If missing, Lo is assumed to be 0.
 Hi
 is the xdomain upper limit. If missing, Hi is assumed to be 1.
 Return
 is a number that determines the type of return value: 1 (or missing) = CLogLog, 2 = Inverse CLogLog.
Return Description 1 or omitted CLogLog Transform 2 The inverse of the CLogLog Transform
Remarks
 The X value(s) must be between Lo and Hi (exclusive).
 The complementary loglog link function is commonly used for parameters that lie in the unit interval.
 The standard complementary loglog transformation is defined as follows:
$$y=\textit{CLogLog}(x)=ln{(ln{(1x)})}$$ And,
$$x=\textit{CLogLog}^{1}(y)=1e^{e^y}$$
Where:
 $x_{t}$ is the input value of the input time series at time $t$. X must be between 0 and 1, exclusive.
 $y_{t}$ is the transformed complementary loglog value at time $t$.
 $\textit{CLogLog}^{1}(y)$ is the inverse complementary loglog function.
 To support a generic interval (a, b), we perform the following mapping:
$$z=\frac{x  a}{b  a}$$ So, the revised transform function is expressed as follows:
$$y=\ln{(\ln{(\frac{bx}{ba})})}$$ The inverse transform is expressed as follows:
$$e^y=\ln{(\frac{bx}{ba})}\Rightarrow x=b(ba)e^{e^y}$$  The transform firstorder derivative is calculated as follows:
$$\frac{dy}{dx}=\frac{1}{(ba)\ln{\frac{bx}{ba}}}$$  The transform firstorder derivative (i.e., $\frac{dy}{dx}$ is positive for all xvalues and goes to infinity as x approaches the interval endpoints.
 In essence, the complementary loglog function converts a bounded xrange from (Lo, Hi) to $(\infty, \infty)$.
 Unlike Logit and Probit, the complementary loglog transform is asymmetrical.
Examples
Example 1:


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.
 Hastie, T. J.; Tibshirani, R. J. (1990). Generalized Additive Models. Chapman & Hall/CRC. ISBN 9780412343902.
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