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June 29

dependency with a fractional exponent

If y is dependent on x through a proportional constant, we say that's a linear dependency. If y is proportional to x², it's quadratic; for xⁿ we'd say polynomial. What about something like x^1.57238? "Polynomial" might still be accurate in the computation complexity-theoretic sense, but in other contexts (this is about statistics, if it matters) it seems to me that it connotes an integer exponent. Is there some other word for this sort of relationship? Thanks. 208.70.31.206 (talk) 01:49, 29 June 2009 (UTC)[reply]

If y=x^α, we may simply say that the logarithms of x and y are proportional, or that x and y are proportional in logarithmic scale. The natural expression would be that they are "logarithmically proportional", but I see this is already used, with the meaning "y is proportional to log(x)". (Not very satisfying use, for in this acceptance, "logarithmic proportionality" is not an equivalence). --84.221.69.148 (talk) 06:24, 29 June 2009 (UTC)[reply]

A relationship of the form y = ax^k where k is a constant but not necessarily an integer is generally called a power law. Gandalf61 (talk) 08:18, 29 June 2009 (UTC)[reply]