The equations for the SPT-parameterized semi-bounded metalog distribution are shown below. These equations are implemented in the SPT Metalogs Excel workbook.In this case, the metalog quantile function and pdf, Mlog(y) and mlog(y) respectively, are the n=3 special case of the general semi-bounded metalog equations:
Mlog(y) = bl + eM(y) for 0 < y < 1 = bl for y = 0
mlog(y) = m(y) e-M(y) for 0 < y < 1
= 0 for y = 0
where bl is a user-specified lower bound and
M(y) =
m(y) =
The constants
can be calculated directly from SPT input parameters:
