Summary In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a known mathematical form involving only a finite number of unknown parameters.

No abstract

No abstract

No abstract

We inve.tigate the problem of finding the expected value of function. of a random variable X of the form fIX) = (X+A)---" where X+A> 0 e.s, and n is a non-negative integer. The technique is to succe.sively integrate the probability generating function and i. suggested by the weI/-known result that succe..ive differentiation leads to the positive moment•. The technique is applied to the problem of finding Ell /(x+All for the binomial and Poi..on distributions.