Talk:Metalog distribution

Revision of Jan 6, 2022

Looking at the expansion for μ and s:

$\mu =a_{1}+a_{3}(y-0.5)+a_{5}(y-0.5)^{2}+a_{7}(y-0.5)^{3}+a_{9}(y-0.5)^{4}+\dots$

$s=a_{2}+a_{4}(y-0.5)+a_{6}(y-0.5)^{2}+a_{8}(y-0.5)^{3}+a_{10}(y-0.5)^{4}+\dots$

This seems fine, the subscripts for the a coefficients for μ are 1,3,5,7,.. (all odd) and those for s are 2,4,6,8,... (all even). However the expressions for M_k are then not correct - the a-subscripts for powers of (y-1/2) (corresponding to μ) are 1,4,5,7,9... (4 not 3 ?) and those for terms involving the log (corresponding to s) are 2,3,6,8,... (3 not 4 ?) This seems like an error, but these coefficints are taken directly from Keelin's original paper.

If we call the second set of coefficients "anomalous" then the question is - were these anomalous by choice or was it a typographical error by Keelin which then propagated? Other sites discussing the metalog use these anomalous coefficients, and conclusions about the behavior of the metalog seem to use the anomalous coefficients. Anyway, my first edit used non-anomalous coefficients to "correct" the expressions for M_k but when I realized this is not just a local error but is ubiquitous in the literature, I reverted that edit. I have not yet been able to find any discussion of this "anomaly". PAR (talk) 18:25, 8 January 2022 (UTC)

Dr. Keelin was kind enough to respond to an email that I sent requesting clarification. He pointed me to page 252 of his paper which explains that it was done purposefully and in a way I did not at first understand. Anyway, I have corrected the μ and s expansions and added an explanation for the "anomalous" coefficient order. PAR (talk) 18:25, 8 January 2022 (UTC)