Accurate and unbiased estimation of power-law exponents from single-emitter blinking data

• Published in: The Journal of chemical physics Vol. 125; no. 20; p. 204713
• Main Authors: Hoogenboom, Jacob P, den Otter, Wouter K, Offerhaus, Herman L
• Format: Journal Article
• Language: English
• Published: United States 28.11.2006
• Subjects: Computer Simulation; Fluorescent Dyes - analysis; Fluorescent Dyes - chemistry; Least-Squares Analysis; Luminescent Measurements - methods; Models, Chemical; Models, Molecular; Models, Statistical; Sample Size; Spectrometry, Fluorescence - methods
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.2387165

Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.