PDF / CDF Reference
Quick reference for the relationship between PDF, CDF, exceedance probability and quantiles, with the key formulas for engineering use.
Key formulas
CDF: F(x) = P(X <= x) = integral of f(t) dt from -inf to x
Exceedance: P(X > x) = 1 - F(x)
Quantile: x_p = F^{-1}(p)
PDF: f(x) = dF(x)/dx
Engineering use:
Characteristic strength = F^{-1}(0.05) (5th percentile)
Design load = F^{-1}(0.95) (95th percentile)
Failure probability = P(g < 0)