  In this work, we study the structure of the leading order Martin-Ryskin-Watt
(MRW) unintegrated parton distribution function (UPDF) and explain in detail
why there exists discrepancy between the two different definitions of this UPDF
model, i.e., the integral (I-MRW) and differential (D-MRW) MRW UPDFs. We
perform this investigation with both angular and strong ordering cutoffs. The
derivation footsteps of obtaining the I-MRW UPDF from the D-MRW ones are
numerically performed, and the reason of such non-equivalency between the two
forms is clearly explained. We show and find out that both methods suggested in
the papers by Golec-Biernat and Stasto as well as that of Guiot have
shortcomings, and only the combination of their prescriptions can give us the
same UPDF structure from both of these two different versions of the MRW UPDF,
namely I-MRW and the D-MRW UPDFs.
