Furthermore, the theoretical results are compared with Monte Carlo simulations to validate the derivations of statistics.
Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of N_{i} and N_{j} is g_i/g_j\exp{(E_j-E_i)/kT }, where g_{i,j} are the degeneracy of the state i and that of j, respectively, E_{i,j} their energies, k the Boltzmann constant and T the system's temperature.
From a practical perspective, replication is perhaps as important as the derivation of inferential statistics (if not more so, unless one is particularly concerned with effect size or its equivalent), and it is with this in mind that the results of Study 2 are turned to next.
The construction of such a method entails two tasks: the design of an efficient yet sensitive descriptor model (DM) that acts as a filter, and the derivation of a sensitive statistics covariance model (CM).
Consequences the latter notion has for the derivation of exact distributions of certain statistics have been studied in Müller and Richter (2015, 2016a, b).
A new statistical approach, [40] namely nonextensive statistics or Tsallis statistics based on the derivation of Boltzmann Gibbs Shannon (BGS) entropic measure, [41] is proposed to the study the cases where Maxwell distribution is considered inappropriate.
The approach is based on circumventing the explicit derivation of macroscopic equations for the system statistics (e.g., average coverage).
According to the approximate derivation of the sample distribution in mathematical statistics, coefficient M should be reasonably assigned, depending on the number of encounters of K.
Alternatively, the derivation of regional I/O tables from national statistics tends to compromise data quality such as the applied multipliers and reduces the level of sector disaggregation [24].
We refer the reader to [17] for the derivation of this data-fidelity term using Bayesian statistics.
