It's a Google policy and doesn't share with anybody that how it decides PR of the page. There're many factors which play important role behind the PR but the one and essential thing is the number of quality links points to your website. Where the links come from is also vital like PR, DA, Domain Age and many more.
No.Google already share the calculation formula of Page rank.
This is the Formula for Page rank Calculation
PR(A) = (1 - d) + d * SUM ((PR(I->A)/C(I))
PR(A) is the PageRank of your page A.
d is the damping factor, usually set to 0,85.
PR(I->A) is the PageRank of page I containing a link to page A.
C(I) is the number of links off page I.
PR(I->A)/C(I) is a PR-value page A receives from page I.
SUM (PR(I->A)/C(I)) is the sum of all PR-values page A receives from pages with links to page A.