Are negative comparative operators like "less" typologically rarer than their positive counterparts?

Question

I'm looking for a reference to the claim that negative comparative operators like "less" are cross-linguistically rarer than their positive counterparts.

Is anyone familiar with this claim, and able to provide a reference? Thanks in advance for any assistance.

EDIT: This question is specifically about the "morphosyntactic inventories" of the world's languages -- are negative comparative operators (e.g. "less") more marked than positive ones. In saying this, I intend to distinguish my question from questions about whether speakers tend to avoid negative comparisons in preference of positive ones (e.g. avoiding "X is shorter than Y" in favor of "Y is taller than X").

Answer 1

This is to the now edited question:

It maybe surprising for speakers of Standard Average European languages that so-called "particle comparatives" are rare among the languages of the world, most of the languages use other means to express comparison. For an introduction, see WALS, Chapter 121. Unfortunately, WALS does not provide data on positive/negative comparison.

Note also, that German lacks a positive comparison operator in the strict sense, you just say Peter ist größer als Paul using the comparative form of the adjective in question. You can say (altho' this is a marked construction, the use of kleiner is more natural) Paul ist weniger groß als Peter with a negative comparison operator. Imitating English or French and saying *Peter ist mehr groß als Paul is ungrammatical for German.

Answer 2

Just a quick test using Wortschatz at Leipzig University

Some examples from German language mehr "more" vs. weniger "less"; größer "bigger" vs. kleiner "smaller"

 Wort: mehr Anzahl: 820,965 Rang: 55 Häufigkeitsklasse: 4 
 Wort: weniger Anzahl: 125,207 Rang: 288 Häufigkeitsklasse: 7
 Wort: größer Anzahl: 16,693 Rang: 2,393 Häufigkeitsklasse: 10 
 Wort: kleiner Anzahl: 22,824 Rang: 1,752 Häufigkeitsklasse: 9 

The pair größer/kleiner seems to contradict the intuition, but there a lots of non-comparative uses of the two words, specially of kleiner (e.g., ein kleiner Frechdachs). Testing with the comparison particle als restores the ranks:

 Wort: größer als Anzahl: 3,393 Rang: 10,121 Häufigkeitsklasse: 12 
 Wort: kleiner als Anzahl: 1,325 Rang: 21,873 Häufigkeitsklasse: 13 

So, the claim seems to be supported by the available data. Unfortunately I have no references on who formulated the claim first (although I think it is a well-known claim in the linguistic community). I am also not aware of a catchy name given to this claim.