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# st: re: Cumulative Accuracy Profile

 From Drosophilia Melanogaster To statalist@hsphsun2.harvard.edu Subject st: re: Cumulative Accuracy Profile Date Thu, 3 Feb 2011 13:52:06 +0800 (SGT)

```How does one program an algorithm that estimates the concavity of a Cumulative Accuracy Profile (CAP) curve? I wish to fit a model for y using the function:

y = [1- exp(-kx)]/[1-exp(-k)]

where k is my parameter of interest and is obtained by minimizing a root mean square  error (RMSE) of the form:

e = sqrt{(1/N)*summation i to n of [y_i - [1- exp(-kx_i)]/[1-exp(-k)]]^2}.

The RMSE is minimized by applying a Newton-Raphson procedure using the following iteration (i=1,2... 20):

k_i+1 = k_i - [(de/dk)/(d2e/dk2)]     (ratio of derivatives)

Any help will be greatly appreciated as I am really at a loss when it comes to programming. >__<

Warm regards,

Mika

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