Table 1.
Asymptotic percentage points for Cramer-von Mises statistics.
Table 2.
Distributions used in the simulation study.
Fig 1.
Normal(13,400) and Lognormal(2,1) results.
Simulated power for the tests and simultaneous confidence intervals when data are generated from Normal(13,400) and Lognormal(2,1) distributions for three sample sizes.
Fig 2.
Exponential(.2) and Cauchy(1) results.
Simulated power for the tests and simultaneous confidence intervals when data are generated from Exponential(.2) and Cauchy(1) distributions for three sample sizes.
Fig 3.
Contaminated Benford distribution test results.
Simulated power for the tests when data are generated from the Contaminated Benford distribution where digits 1 and 9 are contaminated by an additive amount γ and for three sample sizes.
Fig 4.
Generalized Benford distribution results.
Simulated power for the tests and simultaneous confidence intervals when data is generated from the Generalized Benford distribution with various values of γ and for two sample sizes.
Fig 5.
Uniform/Benford mixture distribution results.
Simulated power for the tests and simultaneous confidence intervals when data are generated from the Uniform/Benford mixture distribution with various values of γ and for two sample sizes.
Table 3.
Simulated size of tests.
Fig 6.
Contaminated Benford distribution CI results.
Simulated power for the simultaneous confidence intervals when data are generated from the Contaminated Benford distribution where digits 1 and 9 are contaminated by an additive amount γ and for three sample sizes.
Table 4.
Estimated coverage probabilities for Simultaneous Confidence Intervals Law.
Table 5.
Observed digit frequencies and Goodman simultaneous confidence intervals for genomic data.
Table 6.
P-values for tests of the null hypothesis of Benford’s Law for genomic data.
Fig 7.
Goodman simultaneous confidence intervals for the genomic data.
Vertical line segments denote the Goodman simultaneous confidence intervals computed from the Genomic data in Table 5. The red crosses are positioned at the Benford probabilities.
Table 7.
Tests and simultaneous intervals results for the Rodriguez data.
Fig 8.
Goodman simultaneous confidence intervals for the Rodriguez data.
Vertical line segments denote the Goodman simultaneous confidence intervals computed from the Rodriguez data. The red crosses are positioned at the Benford probabilities. The sample size for each data set is given in brackets in the heading.