A family of kinetic distributions for interpretation of experimental fluctuations in kinetic problems

- Gaussian distributions may not be appropriate to describe experimental fluctuations in kinetic experiments.
- Kinetic error distributions are developed to describe fluctuations of conversions more accurately in kinetic problems.
- Analytical and numerical procedures are proposed and used for generation of the new kinetic error distributions.
- The kinetic distribution can provide better fits for analyses of conversion errors.

The computation of confidence intervals frequently leads to arguable results due to lack of rigor when experimental errors are analyzed in kinetic experiments. Particularly, the usual Gaussian approach may not be adequate when the variable of interest is the reactant conversion, as this variable is constrained between very hard limits: 0 and 1. For this reason, the present work focuses on the development of analytical and numerical procedures for more accurate description of experimental errors in first-order reaction systems, which can be eventually extended to more complex reaction processes. Based on the proposed analytical and numerical schemes, new statistical distributions (named here as the kinetic distributions) can be derived to allow for more appropriate representation of conversion fluctuations and the respective statistical quantities, including the confidence intervals, which can be used more advantageously for analyses of kinetic data. In particular, it is shown that conversion errors are heteroscedastic, going through a point of maximum when conversion is allowed to increase from 0 to 1, and that confidence intervals are not symmetrical in respect to the averages, as assumed by Gaussian analyses.

33