1. The ranges of generalized Poisson $$f_{1}(x)$$, cross-over, and power-law $$f_{2}(x)$$ are [1,E], [B,E], and [B,max(x)] respectively. The fitting function is $$f(x)=q(x) s f_{1}(x) +(1-q(x))f_{2}(x)$$, where $$q(x)=\mathrm{e}^{ - (x -B)/(E-x ) }$$. The fitting processes are: obverse proper G and P; calculate parameters of $$sf_{1}(x)$$ (i.e. a, b, s) and $$f_{2}(x)$$ (i.e. c, d) through regressing the empirical distribution in [1,G] and [P,max(x)] respectively; find B and E through exhaustion to make f(x) pass KS test (p-value>0.05). The sum of each f(x) over [1,max(x)] is near unity, which means that f(x) can be regarded as a probability density function.
1. The ranges of generalized Poisson $$f_{1}(x)$$, cross-over, and power-law $$f_{2}(x)$$ are [1,E], [B,E], and [B,max(x)] respectively. The fitting function is $$f(x)=q(x) s f_{1}(x) +(1-q(x))f_{2}(x)$$, where $$q(x)=\mathrm{e}^{ - (x -B)/(E-x ) }$$. The fitting processes are: obverse proper G and P; calculate parameters of $$sf_{1}(x)$$ (i.e. a, b, s) and $$f_{2}(x)$$ (i.e. c, d) through regressing the empirical distribution in [1,G] and [P,max(x)] respectively; find B and E through exhaustion to make f(x) pass KS test (p-value>0.05). The sum of each f(x) over [1,max(x)] is near unity, which means that f(x) can be regarded as a probability density function.