fitting

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fitting

1. an accessory or part
2. work carried out by a fitter

Fitting

 

in statistics, a method by means of which we obtain an analytic and graphic expression of the statistical regularity on which a given empirical series of statistical data is based. By means of fitting, the broken line of the steps of an empirical series is replaced with a smooth, “fitted” curve (in particular cases, with a straight line) and the equation of this curve is computed. During fitting, the following three problems are solved in sequence: the type of equation (shape of the smooth curve) is selected, the parameters (coefficients) of this equation are computed, and the levels (ordinates) of the “theoretical” statistical series obtained are computed (on the basis of the equation) or measured (by the graph of the curve). The type of equation and, correspondingly, the shape of the smooth curve are selected on the basis of general in-formation about (or frequently from practical experience with) the essence of the phenomenon, the regularities of its structure and development, the relationships among its attributes, and so forth (so-called analytic fitting). Where such advance information is not available, the type of equation (shape of the curve) can often be suggested by the graphic shape of the broken line that expresses the given empirical series.

In socioeconomic statistics, fitting is used in three typical cases: (1) fitting a series of distributions, (2) fitting broken lines of regression, and (3) fitting series in a dynamic process.

The purpose of fitting series of distributions is to give quantitative and graphic expressions for the nature of the regularity of the distribution of units of the aggregate on the basis of an assigned attribute (for example, their normal distribution and distribution according to Poisson’s law). In this we preserve the equality of certain primary numerical characteristics of the given empirical series and the theoretical series obtained: the average magnitude of the attribute, the mean quadratic deviation, and the total number of units in the aggregate. We use a particular goodness-of-fit test to establish the degree to which the levels (ordinates) of the theoretical series obtained correspond in aggregate to the empirical steps. In some special cases, for example when fitting population distribution by age given in the census, specially developed procedures and formulas are used to eliminate the well-known “accumulation of ages” ending in 0 and 5. Fitting distributions always assumes the availability of a sufficiently numerous empirical series of data.

Fitting broken lines of regression is done when studying the relationships of attributes in order to obtain a smooth line of regression and a regression (correlation) equation that ex-presses the dependence of the average values of one attribute on values of others; for example, yx = a + bx; yx,z = a + bx + cz.

We resort to fitting time series in dynamic processes to obtain an equation (and a smooth line) expressing the developmental trend of a process in time t; for example, y = a + bt, y = a + bt + ct2. In the last two cases of fitting, the coefficients a, b, c, … of the unknown equation are usually computed by the method of least squares. The fitting of statistical time series should not be confused with smoothing statistical series.

REFERENCES

Huntington, E. V. “Vyravnivanie krivykh po sposobu naimen’shikh kvadratov i sposobu momentov.” In Matematicheskie melody v statistike. Collection of articles edited by H. L. Rietz. Translated and reworked by S. P. Bobrov. Moscow, 1927. Pages 147-61.
Ezhov, A. I. Vyravnivanie i vychislenie riadov raspredelenii. Moscow, 1961.
Khotimskii, V. I. Vyravnivanie statisticheskikh riadov po metodu naimen’shikh kvadratov (sposob Chebysheva). Moscow-Leningrad, 1925. Second ed., Moscow, 1959.
Chetverikov, N. S. “O tekhnike vychisleniia parabolicheskikh krivykh.” In Voprosy kon“iunktury, vol. 2. Moscow, 1926. Reprinted in Chetverikov’s book Statisticheskie i stokhasticheskie issledovaniia. Moscow, 1963. Pages 190-210.
Iastremskii, B. S. Nekotorye voprosy matematicheskoi statistiki. Moscow, 1961. Chapter 2.
Obukhov, V. M. “K voprosu o nakhozhdenii uravneniia regressii, udoletvoriaiushchego dannomu empiricheskomu riadu.” Trudy TsSU, vol. 16, issue II. Moscow, 1923.

F. D. LIVSHITS

fitting

[′fid·iŋ]
(building construction)
(engineering)
A small auxiliary part of standard dimensions used in the assembly of an engine, piping system, machine, or other apparatus.

fitting

fittings, 1
1. A pipe part, usually standardized, such as a bend, coupling, cross, elbow, reducer, tee, union, etc.; used for joining two or more sections of pipe together. The term usually is used in the plural.
2. An accessory such as a bushing, coupling, locknut, or other part of an electric wiring system which is intended to perform a mechanical rather than an electrical function.
3. Same as window hardware.
4. British for luminaire.
5. A decorative or functional item or component in a building which is fixed but not built in; also called a fitment.
References in periodicals archive ?
Margalit is what I call a "negative" fittingness theorist, focusing on what conduct we must avoid if we do not wish to insult others.
Thus, the punishment "due to sin" refers to the "ratio" or "proportion," the fittingness, the "belonging" of the punishment to the infraction, not the fact that it is outstanding.
However, a closer look at both of these passages leaves me unsure that it would be correct to attribute even a rudimentary affirmative theory of fittingness to Murphy.
With regard to the fittingness of the social work activities queried, the respondents identified three types of activity activities as fitting.
Four additional criteria are proposed and described, namely, compellingness, saturation, prompt to action, and fittingness.
If he at times seems to adhere to a superstructure of traditional meaning (sequence, fittingness, progression, the salesman peddling his wares), it is again the wry magician playing with us, a comic, somewhat mad commentary on the frailty of our securities.
And that is not a comment on the fittingness of the Pope to be granted a tribute at a club in a town with a significant Roman Catholic population.
In this fittingness of functions, places and ways of being there is no place for a void.
In evaluating Sartre's approach to narrative reconstruction, Thomas Flynn characterizes the central principle as one of "aesthetic fittingness": "A fittingness," as he says, "to the facts, no doubt, and to the agent's totalizing praxis; but fittingness also to Sartre's political-moral project as committed historian.
Such generalizations are based on the conceptual power of the findings derived from the fittingness and comparability of the cases studied (Firestone, 1993; Schofield, 1993).
It is this very difficulty of proving God's existence that provides Thomas with one of his major arguments for the fittingness of Revelation.
Fittingness is defined as the degree of congruence between sending and receiving contexts" (p.