intuitive understanding of (1+parameter)/parameter

Question

When looking at a function that contains term (1+parameter)/parameter, should there be an intuitive understanding for why this term is included. For example if a function for fishing mortality includes this term and "parameter" is a a growth parameter for fish, is there something I can say about the function with regard to fish growth? Why is the value 1 added to parameter in the numerator?

Sean Owen · Answer

I'm not sure, without knowing more, but this is of course equal to $1 + frac{1}{parameter}$. Out of curiosity I searched for something about fish mortality and growth params and found http://www.fao.org/tempref/docrep/fao/008/a0212e/a0212E08.pdf which sets this up as a log-log regression in terms like a growth param $L_infty$, which makes sense if there's some power-law distribution.

Maybe the parameter being used is its inverse, and it may be that this is fudged with the +1 just to make sure the value is greater than 1 so that the log is nonnegative. Maybe there's a better domain-specific reason for tweaking it.

intuitive understanding of (1+parameter)/parameter

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