Utilities

pl_integral(A,α,b1,b2)

Definite integral of power law $A*x^{-α}$ from b1 (lower) to b2 (upper).

\[\int_{b1}^{b2} \, A \times x^{-\alpha} \, dx = \frac{A}{1-\alpha} \times \left( b2^{1-\alpha} - b1^{1-\alpha} \right)\]

lognormal_integral(μ, σ, b1, b2)

Definite integral of the lognormal probability distribution from b1 to b2.

\[\int_{b1}^{b2} \, \frac{A}{x} \, \exp \left[ \frac{ -\left( \log(x) - \mu \right)^2}{2\sigma^2} \right] \, dx\]