# NDK_CLOGLOG

 int __stdcall NDK_CLOGLOG ( double * X, size_t N, WORD retTYpe )

Computes the complementary log-log transformation, including its inverse.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
 [in,out] X is the univariate time series data (a one dimensional array). [in] N is the number of observations in X. [in] retTYpe is a number that determines the type of return value: 1 (or missing)=C-log-log , 2=inverse C-log-log.
Remarks
1. The complementary log log link function is commonly used for parameters that lie in the unit interval.
2. The complementary log log link/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 link function
• $$\left(x_t +\alpha \right) \gt 0$$ for all t values
3. The BOXCOX function accepts a single value or an array of values for X.
4. The shift parameter must be large enough to make all the values of X positive.
Requirements
Examples



 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_CLOGLOG ( double[] pData, UIntPtr nSize, short argRetType )

Computes the complementary log-log transformation, including its inverse.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
 [in,out] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in pData. [in] argRetType is a number that determines the type of return value: 1 (or missing)=C-log-log , 2=inverse C-log-log.
Remarks
1. The complementary log log link function is commonly used for parameters that lie in the unit interval.
2. The complementary log log link/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 link function
• $$\left(x_t +\alpha \right) \gt 0$$ for all t values
3. The BOXCOX function accepts a single value or an array of values for X.
4. The shift parameter must be large enough to make all the values of X positive.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.DLL
Examples

References
* 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
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848