In AARON CLAUSET’s paper power-law distributions in empirical data: ‘’In practice, few empirical phenomena obey power laws for all values of x. More often the power law applies only for values greater than some minimum x_min. In such cases we say that the tail of the distribution follows a power law.”
So for the data x<x_min, is it necessary to fit with another distribution? If so, the probability density function becomes piecewise and what functions are usually used in such a case? The part x<x_min is about 95% of my data. I find few literature for this problem.