Power-law initial-mass-function tail coordinate
= Power-law initial-mass-function tail coordinate
{title2=$X(M)=(M_{\min}/M)^{p-1}$}
For an <initial mass function> proportional to $M^{-p}$ on $M\ge M_{\min}$ with $p>1$, integration and normalization give the displayed upper-tail fraction. The <probability integral transform> makes $X$ uniform on $[0,1]$ for a randomly sampled birth mass. Evolutionary lifetime regions can then be measured as ordinary areas when the independent age coordinate is also uniform.