Table 1 Statistical distribution functions used in the analysis.

From: Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength

Distribution

PDF

CDF

Lognormal

p(x)=

c(x)=

Exponential

p(x)=λe−λx

c(x)=e−λx

Power law

p(x)=

c(x)=

Rayleigh

p(x)=

c(x)=exp

χ 2

p(x)=xk/2−1e−k/2

c(x)=1−P

Weibull

p(x)=

c(x)=exp

  1. Equations for probability density functions (PDF) and cumulative distribution functions (CDF) of the distributions used in the statistical analysis. The function Γ is the gamma function and P is the regularized gamma function. Parameter xmin is a lower cutoff for the power law distribution, which is either taken to be the lowest dyke thickness value in the data set or is determined as a free parameter23. We do not report results for xmin calculated by the second method since that analysis disregards most of the data.
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