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Just a note

The mean, maximum, and population distribution function are all parameters, as are the standard normal density function (φ) and cumulative function (Φ) - which include their population mean (μ=0) and variance (σ2=1).

In principle a 'function' may be any sort of mathematical or logical procedure that converts, or collates, one set of values to another. The classical mathematical view is of 'mapping' functions, which reversibly rescale or transform a set of values, but the sample mean formula is also a function, as is ranking, and these have no 'inverse functions'.