In the geological paper entitled The power–law relationship between landslide occurrence and rainfall level by C. Li et al, a power-law cumulative probability distribution is derived. However, I don't seem to understand how exactly it was derived. Here's how it follows:
(i) A probability density function $l(R)$ is defined: $$l(R) = \frac{1}{N_{LT}}\frac{\delta N_{L}}{\delta R}$$ where $\delta N_L$ is the number of landslide occurrences at the rainfall level between $R$ and $R+\delta R$, and $N_{LT}$ is the total number of landslides in the inventory.
(ii) The probability of a landslide occurrence at the rainfall level greater than $R$ is $$L(R)=\int\limits_R^\infty l(R')dR'$$
(iii) Substituting $l(R)$ into the integral, they get $$L_{cf}(>R)=CR^{-\beta}$$
How exactly did the substitution process work? I'd appreciate if someone could explain that in steps.