for the default of an R API parameter i seek a function that has the property of yielding a good guess.
- I want the function to be defined for Z+ (But no reason not to define it for R+, i guess)
- I want it to be smooth
It should satisfy both
f(xsmall)=1∀xsmall∈(0,k]
limx→∞f(x)=l
edit to be clear: k and l should be constants appearing in the function definition.
E.g. with k=1000 and l=0, the f(x)=1∀x∈(0,1000]. Then it should gradually decline and approach 0.
To simplify, the function can be written as:
f(x)={1if x≤k[…]otherwise
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