BIAS AND PRECISION IN THE ESTIMATION OF EXPONENTIAL DECAY PARAMETERS FROM SPARSE DATA

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 - 1) for all T and thus can be easily corrected for. The effects of various ways of binning the data are examined for both the ML and LS approaches.