Fig 1.
Iterative flow summarizing major steps and sub-loops. The numbers on procedures and decisions correspond to the pseudo-code for the main loop.
Fig 2.
Comparing quantile plots to their scaled residuals.
For SURD on [0, 1] the corresponding QQ plots (left column) and SQR plots (right column) are shown for increasing sample sizes with N = 28, 212, 216, 220 from top to bottom.
Fig 3.
Probability density for SURD scoring function.
The probability density for the log-likelihood score based on single order statistics for different sample sizes exhibits near sample size invariance. The solid black line is a consensus of all sample sizes combined, and the dashed lines show example levels of SURD coverage.
Fig 4.
Assesment of results for the gamma distribution.
The left column shows the estimated PDF based on four samples colored as green, red, blue and magenta per sample size. Results for different sample sizes are also shown ranging from N = 28, 212, 216, 220 moving from the top to bottom rows. These estimates are compared with the true population PDF shown as a black line. The right column shows the corresponding SQR-plots across respective rows.
Table 1.
Characteristics of PDF estimates for the gamma distribution.
Table 2.
Characteristics of PDF estimates for the bimodal distribution described by a binary mixture of two Gaussian distributions.
Fig 5.
Assesment of results for the sum of two Gaussian distributions.
The data format and coloring is the same as Fig 4.
Table 3.
Characteristics of PDF estimates for a five fingers distribution with a 0.5 weight.
Fig 6.
Assesment of results for the 5-fingers perturbing the uniform distribution with a 0.5 weight.
The data format and coloring is the same as Fig 4.
Fig 7.
Assesment of results for the Cauchy distribution.
The data format and coloring is the same as Fig 4.
Fig 8.
Assesment of results for the discontinuous distribution.
The data format and coloring is the same as Fig 4.
Fig 9.
On a log10-log10 plot, the average CPU time to calculate a model PDF as a function of sample size for all distributions considered here in addition to a few others. The averaging was over 100 distinct solutions per sample size.