Estimation of Ru-97 Half-Life Using the Most Frequent Value Method and Bootstrapping Techniques

Abstract

A new and robust statistics was applied to previous measurements of the 97Ru half-life. This process incorporates the most frequent value (MFV) technique along with hybrid parametric bootstrap (HPB) method to deliver a more precise estimate of the 97Ru half-life. The derived value is T1/2,MFV(HPB) = 2.8385+0.0022-0.0075 days. This estimate corresponds to a 68.27% confidence interval ranging from 2.8310 to 2.8407 days, and a 95.45% confidence interval ranging from 2.8036 to 2.8485 days, calculated using the percentile method. This level of uncertainty is significantly lower-over 30 times-than the uncertainty in the previously recognized half-life value found in nuclear data sheets. Employing an alternate approach to minimization could further cut down the statistical uncertainty by 44% for the 97Ru half-life. In particular, the HPB method accounts for uncertainties in small datasets when determining the confidence interval. When the HPB method, in combination with the MFV approach, was used to review a four-element dataset of the specific activity of 39Ar based on underground data, the result was SA_MFV(HPB) = 0.966 +0.027 -0.020 Bq/kg_atmAr. This value results in a 68.27% confidence interval of 0.946 to 0.993, along with a 95.45% confidence interval of 0.921 to 1.029, also determined using the percentile method.

Figures (8)

• Figure 1: An artificial dataset composed of four elements. The vertical dashed line shows the mean value, whereas the vertical solid line indicates the MFV. The vertical dotted-dashed line represents the weighted average value.
• Figure 2: A histogram was created for each element, which was sampled with replacement from the original dataset, which initially had four elements. The histogram also shows the uncertainty associated with each element.
• Figure 3: A histogram of all the bootstrap data from artificial datasets that contain four elements.
• Figure 4: Histogram showing bootstrap samples for the specific activity of $^{39}$Ar obtained from underground measurements. The thin vertical line indicates the MFV (0.966) for the dataset.
• Figure 5: Decay of $^{97}$Ru in ruthenium at 19K. Experimental data are shown as dots along with error bars. The straight line represents a fit to these data using the R fitting algorithm. Normalized residuals are shown at the bottom of the figure. Out of 116 data points, 80 fall within $\pm$1, and 112 fall within $\pm$2. The normalized residuals seem to be spread out randomly.