Exponential-logarithmic distribution: Difference between revisions

Revision as of 04:19, 6 September 2009

Revision as of 04:20, 6 September 2009

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== Estimation of the parameters ==

To estimate the parameters, EM algorithm is used. This method is discussed in Tahmasbi and Rezaei (2008). The EM iteration is given by

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<math>\beta^{(h+1)}=n\{\sum_{i=1}^n\frac{x_i}{1-(1-p^{(h)})e^{-\beta^{(h)}x_i}}\}^{-1},</math>

: <math>p\beta^{(h+1)} = n \left( \sum_{i=1}^n\frac{x_i}{1-n(1-p^{(h+1)})} e^{ -\ln( pbeta^{(h+1)})x_i}} \sum_right)^{i=-1}^n,</math>

: <math>\betap^{(h+1)}=n\{\sum_{i=1}^n\frac{x_i}{1-n(1-p^{(h+1)})e^} {- \betaln( p^{(h+1)}x_i}}) \}^sum_{-i=1},</math>^n

\{1-(1-p^{(h)})e^{-\beta^{(h)} x_i}\}^{-1}}.</math>