1. Information passed to a subroutine, procedure, or function. The definition of the procedure is written using formal parameters to denote data items that will be provided when the subroutine is called, and the call of the procedure includes corresponding actual parameters. See also parameter passing.
2. A quantity in a function or mathematical model whose value is selected or estimated according to the circumstances. Parameters should be distinguished from constants, which are fixed for all uses of the function or model, and variables, which are the actual recorded measurements involved in the function or model.
Many properties of functions and mathematical models can be deduced from their structural characteristics without reference to particular values; such properties include continuity, differentiality, and linear independence. A function or model for a specific purpose may be formulated by first establishing the appropriate structure (e.g. polynomial, differential equation of a certain form) in which particular values are not yet determined; such values are parameters of the function or model. Various techniques can then be used to find the most suitable value or range of values for the parameters when considering the observed set of data.
For simple models, such as elementary probability distributions, parameters may be estimated from the statistics of the sample, such as the mean and the variance. General principles of estimation, in which the criterion is the agreement between model and data, lead to procedures that may require iterative computing to obtain estimates; important examples are the method of least squares and its generalization, the method of maximum likelihood.
The probability distribution of a parameter estimate is often required, and it is usual to compute its standard deviation, known as its standard error (see measures of variation), its correlation with other parameter estimates, and its confidence limits where appropriate (see confidence interval).
pa·ram·e·ter / pəˈramitər/ • n. technical a numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation: the transmission will not let you downshift unless your speed is within the lower gear's parameters. ∎ Math. a quantity whose value is selected for the particular circumstances and in relation to which other variable quantities may be expressed. ∎ Statistics a numerical characteristic of a population, as distinct from a statistic of a sample. ∎ (in general use) a limit or boundary that defines the scope of a particular process or activity: they set the parameters of the debate.