regressions seems to be the term used more than declining in statistical analysis

When I did undergraduate mathematics, the first expression I learned for this concept was "monotone in-/decreasing function". I thought at the time that this was a little ungramamtical, and, when I later observed that the term "monotonically in-/decreasing" also occurs quite frequently in the literature, I was relieved and resolved to use it in preference to its grammatically suspect cousin.

A monotonically decreasing function is one that never goes up--it either stays the same or goes down. If it's monotonically *strictly* decreasing, then it doesn't even stay the same, but always goes down.

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Note added at 38 mins (2004-11-25 16:16:26 GMT)
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(I shoud add that \"mit e(m,n)\" may change the translation. Maybe \"the function [formula] which is monotonically decreasing in e(m,n)\". I can\'t be 100% sure about this without seeing the formulae.)

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Note added at 44 mins (2004-11-25 16:22:14 GMT)
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Oops! \"should\" above.

For those people who haven\'t grown out of counting Googlies, I will quote the following figures:
monotonously-decreasing-fucntion: 512
monotonic-decreasing-function: 3,040
monotone-decreasing-function: 3,550
monotonically-deccreasing-function: 16,200

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Note added at 50 mins (2004-11-25 16:27:44 GMT)
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And for increasing functions:
-ously: 626
-onic: 4,800
-one: 6,590
-onically: 24,300

And to anyone who would suggest that the figures for \"increasing\" are irrelevant, I would point out that the two concepts are symmetrical and interdefinable and usually defined together.

This discussion reminds me of another that we had a while back with regard to the use of Anglophone and Anglophonic. May I now offer the following:

The structure of the phrase monotonic decreasing function consists of an adjective (monotonic), a present participle used as an adjective (decreasing), and a noun (function). In mathematics there exist both monotonic functions and decreasing functions. Thus, it should be of no surprise to anyone to learn that there also exists something called monotonic decreasing functions.

If only grammarians knew how to write!

Cheers,
and
Happy Thanksgiving Day
from Hong Kong!

Hamo



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Note added at 1 hr 13 mins (2004-11-25 16:50:35 GMT)
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Disclaimer: My full use of this and other forums has been restricted for reasons unknown, so please forgive my lack of direct support for answers offered by other contributors and critical assessment of non-contributors who are misleading and/or abusive.


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Note added at 8 hrs 38 mins (2004-11-26 00:16:28 GMT)
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With regard to the behavior of the function, its value can be monotonically decreasing with regard to a single variable or with regard to all variables. Alternatively, c(m,n) may not even be the functional value in question, as the value of c which is defined by m and n, may be a variable to another function whose value is monotonically decreasing. By way of example, g = f(c(m,n)) where m and n determine the value of c, and c determines the value of g via the function f(c).

In effect, Richard Benham\'s remark with regard to the function\'s further particulars is tangential to the translation in question.