Estimation of equivalent dose and its uncertainty in the OSL SAR protocol when count numbers do not follow a Poisson distribution

The current work focuses on the estimation of equivalent dose and its uncertainty using the single aliquot regenerative protocol in optically stimulated luminescence measurements. The authors show that the count numbers recorded with the use of photomultiplier tubes are well described by negative binomial distributions, different ones for background counts and photon induced counts. This fact is then exploited in pseudo-random count number generation and simulations of D_e determination assuming a saturating exponential growth. A least squares fitting procedure is applied using different types of weights to determine whether the obtained De's and their error estimates are unbiased and accurate. A weighting procedure is suggested that leads to almost unbiased D_e estimates. It is also shown that the assumption of Poisson distribution in D_e estimation may lead to severe underestimation of the D_e error.