Where does parameter collide?

In statistics a parameter is a fixed numerical characteristic of an entire population, such as its true mean or its variance: it is a constant of the population that is usually unknown and can only be estimated from a sample, and it is kept sharply apart from a statistic, the matching quantity computed from the observed data. Fisher's 1922 On the mathematical foundations of theoretical statistics drew this line, treating the observations as a sample drawn from a hypothetical population whose distribution is fixed by a few parameters to be estimated. The referent is a fixed but hidden property of a whole population, a single true number standing behind the data, not a variable that traces out a curve or a named slot inside a piece of code.[1]

Unit

One fixed population constant, such as a true mean or variance, on the scale of the measured quantity

Recovery means

Not applicable

Measured by

Never observed directly; estimated from sample data by an estimator whose computed value is a statistic

In mathematics a parameter is an independent quantity that indexes a family of objects or traces out a curve, held fixed within any one case but free to vary from case to case: in parametric equations a point's coordinates x(t) and y(t) are each given as functions of a parameter t that runs along the curve, and a family of functions can likewise be labelled by a parameter that picks out one member. Courant and John's Introduction to Calculus and Analysis (1999 reprint of their classic text) develops this parametric representation of curves and the role of such an auxiliary variable. The referent is a free indexing variable internal to a mathematical description, a dial that selects or sweeps, not a hidden population constant or a named input to a subroutine.[2]

Unit

One auxiliary variable that ranges over a family of objects or along a curve

Recovery means

Not applicable

Measured by

Not measured; assigned or swept over its range to generate or select the members of a family

In computer science a parameter is a named variable declared in the definition of a function or subroutine, a placeholder that receives a value when the routine is called: the parameter written in the definition is the formal parameter, and the actual value supplied at the call is the argument, so the parameter-versus-argument distinction separates the slot from what fills it. The 1960 Report on the algorithmic language ALGOL 60 by Backus and colleagues formalised formal parameters and the rules for binding arguments to them at each call. The referent is a named input slot inside a program's code, filled fresh every time the routine runs, not a fixed population constant or a variable that sweeps out a curve.[3]

Unit

One named input slot in a routine's definition, bound to an argument at each call

Recovery means

Not applicable

Measured by

Not measured; declared in code and bound to an argument value when the routine is invoked