Pineau and Mudry have provided some interesting points of discussion to a recent paper**. The present note offers some further discussion of the points raised. Statistical evidence is presented that the new two-parameter function of the present author [1] does indeed fit the data which has already been shown much better than the [3].
The conservatism of one function with respect to another is difficult to assess since it depends somewhat on the basis of comparison. Comparison based on the mean as in the original paper seems sensible since the mean is a fundamental characteristic of the data. Another problem is that if J1o (proportional to K 2) is considered the square root of the mean J will not be the same as mean K.
The new function is always (positively) skewed toward low values (majority of results below the mean), whereas the Weibull function with shape parameter four is (negatively) skewed towards high values (majority of results above the mean). This difference between skewnesses leads to the type of (non-)conservatism discussed originally.
Comparison of Fig. of with Fig. of [7] also provides support for our original contention. The fit of the new function in Fig. of [1] has a coefficient of correlation of 0.993 whereas the fit of the Weibull function to the same data has a coefficient of correlation off 0.978; thelikelihood that this difference occurs by chance is only 0.13 percent (see, for example, p.413 of [8]), so one infers with 99.8 percent confidence that the new function is better than the Weibull function for this data. The least-squares fit of Fig. of shows non-conservatism of the fitted line for medium values of J. The fit of the new function is good and therefore neither conservative nor non-conservative.