Parameter

A parameter (from Ancient Greek παρά (pará) 'beside, subsidiary' and μέτρον (métron) 'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.).

Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.

For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and the viscosities (for fluids), appear as parameters in the equations modeling movements.

For example, if one were considering the movement of an object on the surface of a sphere much larger than the object (e.g. the Earth), there are two commonly used parametrizations of its position: angular coordinates (like latitude/longitude), which neatly describe large movements along circles on the sphere, and directional distance from a known point (e.g. "10km NNW of Toronto" or equivalently "8km due North, and then 6km due West, from Toronto" ), which are often simpler for movement confined to a (relatively) small area, like within a particular country or region.

In some informal situations it is a matter of convention (or historical accident) whether some or all of the symbols in a function definition are called parameters.

More formal presentations of such situations typically start out with a function of several variables (including all those that might sometimes be called "parameters") such as as the most fundamental object being considered, then defining functions with fewer variables from the main one by means of currying.

[Kilpatrick quoting Woods] "Now ... the engineers ... change the lever arms of the linkage ... the speed of the car ... will still depend on the pedal position ... but in a ... different manner.

These are of the form In this formula, t is the argument of the function F, and on the right-hand side the parameter on which the integral depends.

In statistics and econometrics, the probability framework above still holds, but attention shifts to estimating the parameters of a distribution based on observed data, or testing hypotheses about them.

, can be used as an estimate of the mean parameter (estimand), denoted μ, of the population from which the sample was drawn.

It is possible to make statistical inferences without assuming a particular parametric family of probability distributions.

For example, a test based on Spearman's rank correlation coefficient would be called non-parametric since the statistic is computed from the rank-order of the data disregarding their actual values (and thus regardless of the distribution they were sampled from), whereas those based on the Pearson product-moment correlation coefficient are parametric tests since it is computed directly from the data values and thus estimates the parameter known as the population correlation.

The parameter λ is the mean number of observations of some phenomenon in question, a property characteristic of the system.

k is a variable, in this case the number of occurrences of the phenomenon actually observed from a particular sample.

For instance, suppose we have a radioactive sample that emits, on average, five particles every ten minutes.

(In casual usage the terms parameter and argument might inadvertently be interchanged, and thereby used incorrectly.)

These concepts are discussed in a more precise way in functional programming and its foundational disciplines, lambda calculus and combinatory logic.

Tiernan Ray, in an article on GPT-3, described parameters this way: A parameter is a calculation in a neural network that applies a great or lesser weighting to some aspect of the data, to give that aspect greater or lesser prominence in the overall calculation of the data.

[3]In engineering (especially involving data acquisition) the term parameter sometimes loosely refers to an individual measured item.

The term is used particularly for pitch, loudness, duration, and timbre, though theorists or composers have sometimes considered other musical aspects as parameters.

The term is also common in music production, as the functions of audio processing units (such as the attack, release, ratio, threshold, and other variables on a compressor) are defined by parameters specific to the type of unit (compressor, equalizer, delay, etc.