Left truncation incorrectly handled in fr(), the pdf of point transect distances?

[fpetersma]

The function distpdf() returns the (non-normalised) probability density function for distances. In turn, this function then calls fx() in case of line transect data, and fr() in case of point transect data. fx() calls detfct() and divides it's output by (width - left), i.e., it divides it by the distance from the left trunctation distance to the right truncation distance. On the other, fr() calls detfct() and tries to correct it for point transects, however, it does not take the left truncation distance into account. In a meeting today with @lenthomas and @erex we felt that this is incorrect and that the left truncation distance should be used here one way or another.

[lenthomas]

There is a general "left truncation" theme building up here. Other relevant issues are

• monotonicity warnings
• similar issue as above, effectively
• There is an inconsistency between how mcds.exe handles left truncation and how mrds does it. It's to do with whether you (a) estimate P_a from 0 to w and then the surveyed area is 2wL or (b) estimate P_a from l to w (where l is left truncation distance) and then the surveyed area is 2(w-l)L. Is it worth bringing consistency to our two implementations?

For discussion at a future DistDev meeting...