Bias and precision in the estimation of exponential decay parameters form sparse data

Journal Article · Sat May 01 04:00:00 EDT 1993 · Analytical Chemistry (Washington); (United States)

DOI:https://doi.org/10.1021/ac00057a022· OSTI ID:6079333

Tellinghuisen, J ^[1]; Wilkerson, Jr, C W ^[2]

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1. Vanderbilt Univ., Nashville, TN (United States)
2. Los Alamos National Lab., NM (United States)

The statistical properties of maximum likelihood (ML) and least-squares (LS) estimators for the exponential decay parameters [Gamma](rate) and [tau] (lifetime) are examined for finite observation time (T) and a small number of counts (N). The ML estimators and their variances are assessed via numerical calculations employing the exact N-point distributions for exponentially distributed random data. Bias is a common feature of all these estimators under these conditions. In addition, the ML lifetime estimator exhibits the interesting property of divergence in its variance, which means that [Gamma] is the statistically preferred parameter for characterizing exponential decay for finite observation time. The bias in [Gamma] is less than N/(N approximately 1) for all T and thus can easily be corrected for. The effects of various ways of binning the data are examined for both the ML and LS approaches. 17 refs., 9 figs.

• OSTI ID: 6079333
• Journal Information: Analytical Chemistry (Washington); (United States), Journal Name: Analytical Chemistry (Washington); (United States) Vol. 65:9; ISSN 0003-2700; ISSN ANCHAM
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400102* -- Chemical & Spectral Procedures
400200 -- Inorganic
Organic
& Physical Chemistry
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
CALCULATION METHODS
DECAY
EMISSION SPECTROSCOPY
FLUORESCENCE SPECTROSCOPY
KINETICS
LEAST SQUARE FIT
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
MONTE CARLO METHOD
NUMERICAL SOLUTION
SPECTROSCOPY