The results of the most challenging CoC for the

log-normal distributions are shown in Figure 7.

Based on the goodness-of-fit test results, Weibull and

log-normal distributions were selected to model [mathematical expression not reproducible], respectively.

To this aim,

log-normal distributions are chosen as they provided a valuable description of knock intensity distribution during several experimental acquisitions.

As can be seen, the

log-normal distribution suitably models the power fluctuations in this case.

Coutant [32] carried out the comparison between the entropy maximizing method, the mixture of

log-normal distribution, and the Gram-Charlier expansion based on three criteria: these are robustness of estimation, convergence speed, and ease of application.

For the

log-normal distribution all moments exist, regardless of the value of the parameters, such that for a coherent risk measure like TVaR, the quantity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] will always be well defined.

Total corrosion Specimen number Alternate times time (h) 1-1 2 320 1-2 2 640 1-3 2 960 1-4 2 1280 1-5 2 1600 1-6 2 1920 Table 6: The evaluating value of [mu], [sigma], [alpha], [beta], b, and r for

log-normal distribution and 3P-Weibull distribution.

Suppose Y has a standard

log-normal distribution with its probability distribution function [PHI], and U is independent of Y and uniformly distributed on (0,1).

Therefore, we constructed the distributions by finding parameters for which a

log-normal distribution would present the relevant value found in the literature, and the 2.5th and 97.5th percentiles would correspond to the ranges found in the literature.

In [18], [19] and [20], by using a

log-normal distribution to substitute the gamma-log-normal distribution, approximate expressions of the ergodic capacity are derived for downlink DAS over shadowed fading channel, where Rayleigh fading and Nakagami fading are respectively considered, but the derived theoretical capacity are not accurate enough to reflect the actual values, and the analysis is limited in single receive antenna case.

Among them, the

log-normal distribution was found here with the best Anderson-Darling statistic.