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.
[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. You have changed a parameter"
The symbols before the semicolon in the function's definition, in this example the 's, denote variables, while those after it, in this example the 's, denote parameters.
Strictly speaking, parameters are denoted by the symbols that are part of the function's definition, while arguments are the values that are supplied to the function when it is used. Thus, a parameter might be something like "the ratio of the cylinder's radius to its height", while the argument would be something like "2" or "0.1".
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.
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". The function defining the distribution (the probability mass function) is:
For instance, suppose we have a 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 will 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, which has as parameters the mean μ and the variance σ².
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.
Statistics are mathematical characteristics of samples which can be used as estimates of parameters, mathematical characteristics of the populations from which the samples are drawn. For example, the sample mean () can be used as an estimate of the mean parameter (μ) of the population from which the sample was drawn.
"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.
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
x is a formal parameter. When the function is used as in
3 is the actual parameter value that is substituted for x, the formal parameter, in the function definition. These concepts are discussed in a more precise way in functional programming and its foundational disciplines, lambda calculus and combinatory logic.
In computing, parameters are often called arguments, and the two words are used interchangeably. However, some computer languages such as C define argument to mean actual parameter (i.e., the value), and parameter to mean formal parameter.
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