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A parameter (), generally, is any characteristic that can help in defining or classifying a particular
system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purp ...

system
(meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
,
computer programming Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a particular task. Programming involves tasks such as analysis, generating algorithms, Profilin ...
,
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...

engineering
,
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
,
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

logic
,
linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as well as the methods for studying ...

linguistics
, electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'.


Modelization

When a
system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purp ...
is modeled by equations, the values that describe the system are called ''parameters''. For example, in
mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million ...

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. There are often several choices for the parameters, and choosing a convenient set of parameters is called ''parametrization''. 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. Such parametrizations are also relevant to the modelization of geographic areas (i.e. map drawing).


Mathematical functions

Mathematical function In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ge ...
s have one or more
arguments In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ...
that are designated in the definition by variables. A function definition can also contain parameters, but unlike variables, parameters are not listed among the arguments that the function takes. When parameters are present, the definition actually defines a whole family of functions, one for every valid set of values of the parameters. For instance, one could define a general
quadratic function In algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In ...

quadratic function
by declaring :f(x)=ax^2+bx+c; Here, the variable ''x'' designates the function's argument, but ''a'', ''b'', and ''c'' are parameters that determine which particular quadratic function is being considered. A parameter could be incorporated into the function name to indicate its dependence on the parameter. For instance, one may define the base-''b'' logarithm by the formula :\log_b(x)=\frac where ''b'' is a parameter that indicates which logarithmic function is being used. It is not an argument of the function, and will, for instance, be a constant when considering the
derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...
\textstyle\log_b'(x) = (x\ln(b))^. 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. However, changing the status of symbols between parameter and variable changes the function as a mathematical object. For instance, the notation for the
falling factorial power In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial :(x)_n = x^ = x(x-1)(x-2)\cdots(x-n+1) = \prod_^n(x-k+1) = \prod_^(x-k). The rising fac ...
:n^=n(n-1)(n-2)\cdots(n-k+1), defines a
polynomial function In mathematics, a polynomial is an expression (mathematics), expression consisting of variable (mathematics), variables (also called indeterminate (variable), indeterminates) and coefficients, that involves only the operations of addition, subtra ...
of ''n'' (when ''k'' is considered a parameter), but is not a polynomial function of ''k'' (when ''n'' is considered a parameter). Indeed, in the latter case, it is only defined for non-negative integer arguments. 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 :(n,k) \mapsto n^ as the most fundamental object being considered, then defining functions with fewer variables from the main one by means of
currying In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
. Sometimes it is useful to consider all functions with certain parameters as ''parametric family'', i.e. as an
indexed family In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
of functions. Examples from probability theory are given further below.


Examples

* In a section on frequently misused words in his book ''The Writer's Art'', James J. Kilpatrick quoted a letter from a correspondent, giving examples to illustrate the correct use of the word ''parameter'':
W.M. Woods ... a mathematician ... writes ... "... a variable is one of the many things a ''parameter'' is not." ... The dependent variable, the speed of the car, depends on the independent variable, the position of the gas pedal.
ilpatrick 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''. You have changed a parameter"
* A
parametric equaliser Equalization is the process of adjusting the balance between frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial f ...
is an
audio filter An audio filter is a frequency dependent amplifier circuit, working in the audio frequency An audio frequency or audible frequency (AF) is a periodic function, periodic vibration whose frequency is in the band audible to the average human, the ...
that allows the
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
of maximum cut or boost to be set by one control, and the size of the cut or boost by another. These settings, the frequency level of the peak or trough, are two of the parameters of a frequency response curve, and in a two-control equaliser they completely describe the curve. More elaborate parametric equalisers may allow other parameters to be varied, such as skew. These parameters each describe some aspect of the response curve seen as a whole, over all frequencies. A
graphic equaliser Equalization is the process of adjusting the balance between frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial f ...
provides individual level controls for various frequency bands, each of which acts only on that particular frequency band. * If asked to imagine the graph of the relationship ''y'' = ''ax''2, one typically visualizes a range of values of ''x'', but only one value of ''a''. Of course a different value of ''a'' can be used, generating a different relation between ''x'' and ''y''. Thus ''a'' is a parameter: it is less variable than the variable ''x'' or ''y'', but it is not an explicit constant like the exponent 2. More precisely, changing the parameter ''a'' gives a different (though related) problem, whereas the variations of the variables ''x'' and ''y'' (and their interrelation) are part of the problem itself. * In calculating income based on wage and hours worked (income equals wage multiplied by hours worked), it is typically assumed that the number of hours worked is easily changed, but the wage is more static. This makes ''wage'' a parameter, ''hours worked'' an
independent variable Dependent and Independent variables are variables in mathematical modeling A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to f ...
, and ''income'' a
dependent variable Dependent and Independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
.


Mathematical models

In the context of a
mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environm ...
, such as a
probability distribution In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, the distinction between variables and parameters was described by Bard as follows: :We refer to the relations which supposedly describe a certain physical situation, as a ''model''. Typically, a model consists of one or more equations. The quantities appearing in the equations we classify into ''variables'' and ''parameters''. The distinction between these is not always clear cut, and it frequently depends on the context in which the variables appear. Usually a model is designed to explain the relationships that exist among quantities which can be measured independently in an experiment; these are the variables of the model. To formulate these relationships, however, one frequently introduces "constants" which stand for inherent properties of nature (or of the materials and equipment used in a given experiment). These are the parameters.


Analytic geometry

In
analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measur ...
,
curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geo ...

curve
s are often given as the image of some function. The argument of the function is invariably called "the parameter". A circle of radius 1 centered at the origin can be specified in more than one form: *''implicit'' form, the curve is all points (''x'',''y'') that satisfy the relation *:x^2+y^2=1 *''parametric'' form, the curve is all points (cos(''t''), sin(''t'')), when ''t'' varies over some set of values, like [0, 2π), or (-∞,∞) *:(x,y)=(\cos t,\sin t) *:where ''t'' is the ''parameter''. Hence these equations, which might be called functions elsewhere are in analytic geometry characterized as parametric equations and the
independent variable Dependent and Independent variables are variables in mathematical modeling A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to f ...
s are considered as parameters.


Mathematical analysis

In
mathematical analysis Analysis is the branch of mathematics dealing with Limit (mathematics), limits and related theories, such as Derivative, differentiation, Integral, integration, Measure (mathematics), measure, sequences, Series (mathematics), series, and analytic ...
, integrals dependent on a parameter are often considered. These are of the form :F(t)=\int_^f(x;t)\,dx. In this formula, ''t'' is the argument of the function ''F'', and on the right-hand side the ''parameter'' on which the integral depends. When evaluating the integral, ''t'' is held constant, and so it is considered to be a parameter. If we are interested in the value of ''F'' for different values of ''t'', we then consider ''t'' to be a variable. The quantity ''x'' is a '' dummy variable'' or ''variable of integration'' (confusingly, also sometimes called a ''parameter of integration'').


Statistics and econometrics

In
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
and
econometrics Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of Econ ...

econometrics
, the probability framework above still holds, but attention shifts to
estimating Estimation (or estimating) is the process of finding an estimate, or approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived ...
the parameters of a distribution based on observed data, or testing hypotheses about them. In frequentist estimation parameters are considered "fixed but unknown", whereas in
Bayesian estimation In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior probability, posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, ...
they are treated as random variables, and their uncertainty is described as a distribution. In
estimation theory Estimation theory is a branch of statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem ...
of statistics, "statistic" or
estimator In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...

estimator
refers to samples, whereas "parameter" or
estimandAn estimand is a quantity that is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, th ...
refers to populations, where the samples are taken from. A
statistic A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population Population typically refers the number of peop ...

statistic
is a numerical characteristic of a sample that can be used as an estimate of the corresponding parameter, the numerical characteristic of the
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...
from which the sample was drawn. For example, the
sample mean The sample mean (or "empirical mean") and the sample covariance are statistic A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes incl ...
(estimator), denoted \overline X, can be used as an estimate of the ''mean'' parameter (estimand), denoted ''μ'', of the population from which the sample was drawn. Similarly, the
sample variance In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expr ...
(estimator), denoted ''S''2, can be used to estimate the ''variance'' parameter (estimand), denoted ''σ''2, of the population from which the sample was drawn. (Note that the sample standard deviation (''S'') is not an unbiased estimate of the population standard deviation (''σ''): see
Unbiased estimation of standard deviationIn statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a statistical popula ...
.) It is possible to make statistical inferences without assuming a particular parametric family of
probability distribution In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
s. In that case, one speaks of ''
non-parametric statisticsNonparametric statistics is the branch of statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social prob ...
'' as opposed to the
parametric statistics Parametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modeled by a probability distribution that has a fixed set of parameters. Conversely a non-parametric model differs prec ...
just described. For example, a test based on
Spearman's rank correlation coefficient 300px, When the data are roughly elliptically distributed and there are no prominent outliers, the Spearman correlation and Pearson correlation give similar values. In statistics Statistics is the discipline that concerns the collection, orga ...
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 In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin w ...
are parametric tests since it is computed directly from the data values and thus estimates the parameter known as the population correlation.


Probability theory

In
probability theory Probability theory is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are containe ...
, one may describe the
distributionDistribution may refer to: Mathematics *Distribution (mathematics) Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distr ...
of a
random variable A random variable is a variable whose values depend on outcomes of a random In common parlance, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no ...
as belonging to a ''family'' of
probability distribution In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
s, distinguished from each other by the values of a finite number of ''parameters''. For example, one talks about "a
Poisson distribution In probability theory and statistics, the Poisson distribution (; ), named after France, French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a f ...
with mean value λ". The function defining the distribution (the
probability mass function In probability Probability is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which th ...
) is: :f(k;\lambda)=\frac. This example nicely illustrates the distinction between constants, parameters, and variables. ''e'' is
Euler's number The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways. It is the base of a logarithm, base of the natural logarithm. It is the Limit of a sequence, limit of ...
, a fundamental
mathematical constant A mathematical constant is a key number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formal ...
. The parameter λ is the
mean There are several kinds of mean in mathematics, especially in statistics. For a data set, the ''arithmetic mean'', also known as arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by ...
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. If we want to know the probability of observing ''k''1 occurrences, we plug it into the function to get f(k_1 ; \lambda). Without altering the system, we can take multiple samples, which will have a range of values of ''k'', but the system is always characterized by the same λ. For instance, suppose we have a
radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus The atomic nucleus is the small, dense region consisting of s and s ...

radioactive
sample that emits, on average, five particles every ten minutes. We take measurements of how many particles the sample emits over ten-minute periods. The measurements exhibit different values of ''k'', and if the sample behaves according to Poisson statistics, then each value of ''k'' will come up in a proportion given by the probability mass function above. From measurement to measurement, however, λ remains constant at 5. If we do not alter the system, then the parameter λ is unchanged from measurement to measurement; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase. Another common distribution is the
normal distribution In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by ex ...

normal distribution
, which has as parameters the mean μ and the variance σ². In these above examples, the distributions of the random variables are completely specified by the type of distribution, i.e. Poisson or normal, and the parameter values, i.e. mean and variance. In such a case, we have a parameterized distribution. It is possible to use the sequence of moments (mean, mean square, ...) or
cumulantIn probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressin ...
s (mean, variance, ...) as parameters for a probability distribution: see
Statistical parameterIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a ...
.


Computer programming

In
computer programming Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a particular task. Programming involves tasks such as analysis, generating algorithms, Profilin ...
, two notions of
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whol ...
are commonly used, and are referred to as
parameters and arguments A parameter (from the Ancient Greek language, Ancient Greek wikt:παρά#Ancient Greek, παρά, ''para'': "beside", "subsidiary"; and wikt:μέτρον#Ancient Greek, μέτρον, ''metron'': "measure"), generally, is any characteristic that ...
—or more formally as a formal parameter and an actual parameter. For example, in the definition of a function such as : y = ''f''(''x'') = ''x'' + 2, ''x'' is the ''formal parameter'' (the ''parameter'') of the defined function. When the function is evaluated for a given value, as in :''f''(3): or, ''y'' = ''f''(3) = 3 + 2 = 5, 3 is the ''actual parameter'' (the ''argument'') for evaluation by the defined function; it is a given value (actual value) that is substituted for the ''formal parameter'' of the defined function. (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 In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of , ...
and its foundational disciplines,
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using variable N ...
and
combinatory logic Combinatory logic is a notation to eliminate the need for Quantifier (logic), quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoreti ...
. Terminology varies between languages; some computer languages such as C define parameter and argument as given here, while Eiffel uses an alternative convention.


Engineering

In
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...

engineering
(especially involving data acquisition) the term ''parameter'' sometimes loosely refers to an individual measured item. This usage isn't consistent, as sometimes the term ''channel'' refers to an individual measured item, with ''parameter'' referring to the setup information about that channel. "Speaking generally, properties are those physical quantities which directly describe the physical attributes of the system; parameters are those combinations of the properties which suffice to determine the response of the system. Properties can have all sorts of dimensions, depending upon the system being considered; parameters are dimensionless, or have the dimension of time or its reciprocal." The term can also be used in engineering contexts, however, as it is typically used in the physical sciences.


Environmental science

In environmental science and particularly in
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

chemistry
and
microbiology Microbiology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...

microbiology
, a parameter is used to describe a discrete chemical or microbiological entity that can be assigned a value: commonly a concentration, but may also be a logical entity (present or absent), a
statistical Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statist ...

statistical
result such as a
95 percentile
95 percentile
value or in some cases a subjective value.


Linguistics

Within linguistics, the word "parameter" is almost exclusively used to denote a binary switch in a
Universal Grammar Universal grammar (UG), in modern linguistics Linguistics is the scientific study of language A language is a structured system of communication Communication (from Latin Latin (, or , ) is a classical language belonging t ...
within a
Principles and Parameters Principles and parameters is a framework within generative linguistics Generative grammar, or generativism , is a linguistic theory that regards linguistics Linguistics is the science, scientific study of language. It encompasses the a ...
framework.


Logic

In
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

logic
, the parameters passed to (or operated on by) an ''open predicate'' are called ''parameters'' by some authors (e.g., Prawitz, "Natural Deduction"; Paulson, "Designing a theorem prover"). Parameters locally defined within the predicate are called ''variables''. This extra distinction pays off when defining substitution (without this distinction special provision must be made to avoid variable capture). Others (maybe most) just call parameters passed to (or operated on by) an open predicate ''variables'', and when defining substitution have to distinguish between ''
free variable In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a Mathematical notation, notation (symbol) that specifies places in an expression (mathematics), expressio ...
s'' and ''
bound variable In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
s''.


Music

In music theory, a parameter denotes an element which may be manipulated (composed), separately from the other elements. The term is used particularly for
pitch Pitch may refer to: Acoustic frequency * Pitch (music), the perceived frequency of sound including "definite pitch" and "indefinite pitch" ** Absolute pitch or "perfect pitch" ** Pitch class, a set of all pitches that are a whole number of octaves ...
,
loudness In acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is ...
,
duration Duration may refer to: * The amount of Time#Terminology, time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a th ...
, and
timbre In music, timbre ( ), also known as tone color or tone quality (from ), is the perceived sound quality of a , sound or . Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables li ...

timbre
, though theorists or composers have sometimes considered other musical aspects as parameters. The term is particularly used in
serial music upright=1.5, Six-element row of rhythmic values used in ''Variazioni canoniche'' by Luigi Nono. In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began pri ...
, where each parameter may follow some specified series.
Paul Lansky Paul Lansky (born June 18, 1944, in New York City, New York) is an American composer. Biography Paul Lansky (born 1944) is an American composer. He was educated at Manhattan's The High School of Music and Art, High School of Music and Art, Queens ...
and
George Perle George Perle (May 6, 1915 – January 23, 2009) was a composer A composer (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area ...
criticized the extension of the word "parameter" to this sense, since it is not closely related to its mathematical sense, but it remains common. 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.).


See also

*
Coordinate system In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

Coordinate system
* Occam's razor (with regards to the trade-off of many or few parameters in data fitting)


References

{{Authority control Mathematical terminology