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Encyclopedia > Parameter
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For usage in computer science and programming, see parameter (computer science).

A parameter is a measurement or value on which something else depends. Image File history File links Stop_hand. ... This article needs to be cleaned up to conform to a higher standard of quality. ...

For example, a parametric equaliser is an audio filter that allows the 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 provides individual level controls for various frequency bands, each of which acts only on that particular frequency band. In audio processing, equalization (EQ) is the process of modifying the frequency envelope of a sound. ... An audio filter is a type of filter used for processing sound signals. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... In audio processing, equalization (EQ) is the process of modifying the frequency envelope of a sound. ...

## Contents

### Mathematical

In mathematics, the difference in meaning between a parameter and an argument of a function is that the parameters are the symbols that are part of the function's definition, while arguments are the symbols that are supplied to the function when it is used. The value or objects assigned to the parameters by the corresponding arguments of a function or system are not reassigned during the function's evaluation. So, parameters are effectively constants during the evaluation or processing of that function or system. The value of arguments can change outside of the function and between function usages. This distinction, the parameter's constancy, is a key part of the meaning of a parameter in any situation, often in usage beyond just mathematics. Euclid, detail from The School of Athens by Raphael. ... Partial plot of a function f. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ...

In some informal situations people regard it as a matter of convention (and therefore a historical accident) whether some or all the arguments of a function are called parameters.

### Computer science

When the terms formal parameter and actual parameter are used, they generally correspond with the definitions used in computer science. In the definition of a function such as This article needs to be cleaned up to conform to a higher standard of quality. ...

f(x) = x + 2,

x is a formal parameter. When the function is used as in

y = f(3) + 5,

3 is the actual parameter value that is used to solve the equation. These concepts are discussed in a more precise way in functional programming and its foundational disciplines, lambda calculus and combinatory logic. Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... Combinatory logic is a notation introduced by Moses SchÃ¶nfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. ...

In computing, the parameters passed to a function subroutine are more normally called arguments. Originally, the word computing was synonymous with counting and calculating, and a science that deals with the original sense of computing mathematical calculations. ...

### Logic

In 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 has to 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 variables and bound variables. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...

### Engineering

In engineering (especially involving data acquisition) the term parameter sometimes loosely refers to an individual measured item. For example an airliner flight data recorder may record 88 different items, each termed a parameter. 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. Engineering is the application of scientific and technical knowledge to solve human problems. ... An example of a Flight Data Recorder The flight data recorder (FDR) is a flight recorder used to record specific aircraft performance parameters. ...

## Analytic geometry

In analytic geometry, curves 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: Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...

• implicit form
x2 + y2 = 1
• parametric form
(x,y) = (cost,sint)
where t is the parameter.

A somewhat more detailed description can be found at parametric equation. Graph of a butterfly curve, a parametric equation discovered by Temple H. Fay In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters. ...

## Mathematical analysis

In mathematical analysis, one often considers "integrals dependent on a parameter". These are of the form Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...

$F(t)=int_{x_0(t)}^{x_1(t)}f(x;t),dx.$

In this formula, t is the argument of the function F on the left-hand side, and the parameter that the integral depends on, on the right-hand side. The quantity x is a dummy variable or variable (or parameter) of integration. Now, if we performed the substitution x=g(y), it would be called a change of variable. In calculus, the substitution rule is a tool for finding antiderivatives and integrals. ...

## Probability theory

In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, distinguished from each other by the values of a finite number of parameters. For example, one talks about "a Poisson distribution with mean value λ", or "a normal distribution with mean μ and variance σ2". The latter formulation and notation leaves some ambiguity whether σ or σ2 is the second parameter; the distinction is not always relevant. Probability theory is the mathematical study of probability. ... In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... A random variable is a term used in mathematics and statistics. ... In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... In probability theory and statistics, the Poisson distribution is a discrete probability distribution. ... The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. ...

It is possible to use the sequence of moments (mean, mean square, ...) or cumulants (mean, variance, ...) as parameters for a probability distribution.-1... // Cumulants of probability distributions In probability theory and statistics, the cumulants Îºn of the probability distribution of a random variable X are given by In other words, Îºn/n! is the nth coefficient in the power series representation of the logarithm of the moment-generating function. ...

## Statistics

In statistics, 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. In classical estimation these parameters are considered "fixed but unknown", but in Bayesian estimation they are random variables with distributions of their own. A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... There are many different ways of discussing statistical estimation. ... One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ... In statistics, confidence intervals are the most prevalent form of interval estimation. ... In the philosophy of mathematics Bayesianism is the tenet that the mathematical theory of probability is applicable to the degree to which a person believes a proposition. ...

It is possible to make statistical inferences without assuming a particular parametric family of probability distributions. In that case, one speaks of non-parametric statistics as opposed to the parametric statistics described in the previous paragraph. For example, Spearman is a non-parametric test as it is computed from the order of the data regardless of the actual values, whereas Pearson is a parametric test as it is computed directly from the data and can be used to derive a mathematical relationship. The branch of statistics known as non-parametric statistics is concerned with non-parametric statistical models and non-parametric statistical tests. ... Parametric inferential statistical methods are mathematical procedures for statistical hypothesis testing which assume that the distributions of the variables being assessed belong to known parametrized families of probability distributions. ... In statistics, Spearmans rank correlation coefficient, named for Charles Spearman and often denoted by the Greek letter Ï (rho), is a non-parametric measure of correlation â€“ that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, without making any assumptions about the frequency... In mathematics, and in particular statistics, the Pearson product-moment correlation coefficient (r) is a measure of how well a linear equation describes the relation between two variables X and Y measured on the same object or organism. ...

Statistics are mathematical characteristics of samples which are used as estimates of parameters, mathematical characteristics of the populations from which the samples are drawn. For example, the sample mean ($overline X$) is an estimate of the mean parameter (μ) of the population from which the sample was drawn. A statistic (singular) is the result of applying a statistical algorithm to a set of data. ...

Results from FactBites:

 Parameter - encyclopedia article about Parameter. (2481 words) In mathematics, the difference in meaning between a parameter and an argument of a function is that the parameters are the symbols that are part of the function's definition, while arguments refer to the symbols that are supplied to the function when it is used. In classical estimation these parameters are considered "fixed but unknown", but in Bayesian estimation they are random variables with distributions of their own. Statistics are mathematical characteristics of samples which are used as estimates of parameters, mathematical characteristics of the populations from which the samples are drawn.
 Parameter - definition of Parameter in Encyclopedia (726 words) In mathematics there is little difference in meaning between a parameter and an argument of a function. It is usually a matter of convention (and therefore a historical accident) whether some or all the arguments of a function are called parameters. On the computer, parameters are used to differentiate behavior or pass input data to computer programs or their subprograms.
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