Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
The percentage of times each distribution fell within the top 3 best-fit candidates for each element of the cascaded random variable ABCD matrix, ⌈, BS-Birnbaum-Saunders_ GEV-Generalized Extreme Value, GP-Generalized Pareto_
| Distribution Name | A | B | C | D | ||||
|---|---|---|---|---|---|---|---|---|
| Magnitude | Phase | Magnitude | Phase | Magnitude | Phase | Magnitude | Phase | |
| Inverse Gaussian | 15.19 | 2.22 | 13.7 | 1.48 | 12.22 | 2.22 | 12.96 | 2.22 |
| BS | 11.85 | 2.22 | 11.48 | 1.85 | 8.15 | 2.22 | 12.22 | 2.22 |
| Lognormal | 15.19 | 2.22 | 15.93 | 1.85 | 12.22 | 2.22 | 12.59 | 2.22 |
| Rician | 8.89 | 4.44 | 9.63 | 2.22 | 2.96 | 6.67 | 9.63 | 4.44 |
| Normal | 8.52 | 10 | 10 | 8.89 | 9.63 | 12.22 | 7.04 | 10 |
| Nakagami | 10 | 4.44 | 10.74 | 2.59 | 10.74 | 6.3 | 11.48 | 4.44 |
| Gamma | 3.7 | 0 | 1.48 | 0.74 | 5.19 | 0 | 5.93 | 0 |
| Log-logistic | 8.89 | 0 | 11.11 | 0 | 8.15 | 0 | 8.52 | 0 |
| Weibull | 4.44 | 0 | 4.44 | 0 | 4.44 | 0 | 4.44 | 0 |
| GEV | 6.67 | 8.89 | 5.56 | 7.78 | 6.67 | 8.89 | 6.67 | 8.89 |
| GP | 4.44 | 22.22 | 0 | 25.56 | 6.3 | 20 | 4.44 | 22.22 |
| Logistic | 1.11 | 5.56 | 1.48 | 4.81 | 2.59 | 4.44 | 1.85 | 5.19 |
| T Location-Scale | 1.11 | 3.33 | 4.44 | 2.22 | 0 | 3.7 | 2.22 | 3.33 |
| Beta | 0 | 0 | 0 | 0.37 | 10.74 | 0 | 0 | 0 |
| Extreme Value | 0 | 17.78 | 0 | 21.11 | 0 | 15.56 | 0 | 17.78 |
| Rayleigh | 0 | 16.67 | 0 | 18.52 | 0 | 15.56 | 0 | 17.04 |
The PDFs assumed for R, G and B_
| PDF Test Case | R | G | B |
|---|---|---|---|
| A | N(2.38E + 03, 2.38E + 03) | N(4.20E − 04, 2.40e − 04) | N(2.85E + 07, 2.85E + 07) |
| B | N(2.38E + 03, 4.76E + 03) | N(4.20E − 04, 8.40E − 04) | N(2.85E + 07, 5.70E + 07) |
| C | N(2.38E + 03, 7.14E + 03) | N(4.20E − 04, 1.26E − 03) | N(2.85E + 07, 8.55E + 07) |
| D | U(0, 2.38E + 03) | U(0, 2.40e − 04) | U(0, 2.85E + 07) |
| E | U(0, 4.76E + 03) | U(0, 8.40E − 04) | U(0, 5.70E + 07) |
| F | U(0, 7.14E + 03) | U(0, 1.26E − 03) | U(0, 8.55E + 07) |
| G | Gamma(2.3810E + 03, 1) | Gamma(4.2000E − 04, 1) | Gamma(2.8501E + 07, 1) |
| H | Gamma(1.1905E + 03, 2) | Gamma(2.1000E − 04, 2) | Gamma(1.4250E + 07, 2) |
| I | Gamma(7.9365E + 02, 3) | Gamma(1.4000E − 04, 3) | Gamma(9.5002E + 06, 3) |