A Maximum Likelihood Method for Power Law Distributions That Does Not Break Down When the Slope Is Close to Unity
- Creators
- Zhu, Zhaoyan
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Marcus, R. A.
Abstract
A general maximum likelihood estimation (MLE) method is given to analyze experimental data with a power law form with any power exponent which does not break down for a power close to −1. It contrasts thereby with a standard procedure that does. It can be extended to a power law with an exponential tail and more generally to other distribution forms. Inasmuch as the theoretical value of the power for dye-sensitized charge recombination in semiconductors systems, and for certain charge injection, is −1 (Chen, W.; Marcus, R. A., J. Phys. Chem. C, accepted), the present correction to the current MLE method has immediate application to the data in these systems, but it is equally applicable to other systems, regardless of whether the power is −1.
Additional Information
© 2012 American Chemical Society. Received: April 17, 2012. Revised: June 1, 2012. Publication Date (Web): June 7, 2012. We acknowledge the support of this research by NSF, ARO, and ONR and thank Prof. Monti for providing the original experimental data on which Figures 1 and 2 are based. We use data given in ref 30 here, but to be more precise we have the original data from Prof. Monti to verify. This paper was published on the Web on June 20, 2012. Corrections have been made to Reference 1. The correct version was reposted on June 25, 2012.Attached Files
Published - Zhu2012p19034J_Phys_Chem_C.pdf
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Additional details
- Eprint ID
- 32964
- Resolver ID
- CaltechAUTHORS:20120807-084455644
- NSF
- Army Research Office (ARO)
- Office of Naval Research (ONR)
- Created
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2012-08-07Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field