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 ?
It has been observed that excessive quantity of water is leaked due use of non-standard water fittings by Sri Lankan water consumers.
Each section lists the tubing material that works best with each particular fitting. Semi-rigid tubing like nylon, polyethylene and hard durometer polyurethane works well with push-to-connect fittings.
Farm machinery made from the 1930s until the present day has always been a heavy user of grease fittings. With wheels and coulters, a plow might have only a few, but a threshing machine or combine seemed to have a hundred (especially when you were all but standing on your head trying to reach each one, wipe it clean and slip the nozzle of a grease gun on the thing straight enough so the grease would go into the bearing, rather than squirting out to the side).
Some traditional fitting techniques work to correct fit issues, but with today's changing body and fit dynamics, there's often more to fitting than adjusting the pattern edge or cutting apart a muslin.
The LED light fittings can therefore be installed in Zone 1 and 2 hazardous gas areas on ships, oil platforms.
Concurrently with the takeover, the investor also announced a reorganisation of the fittings business area, aimed at enhancing special expertise and product knowledge, through the separation of the furniture fittings and construction fittings businesses.
Along with a 45-degree "street" fitting, you can use a Y-fitting to run vertical drainpipes into horizontal pipes as shown.
Figure 5B shows that the vertical load-carrying capacity of the pipe has been significantly reduced with the usage of the compression fitting. Because of the limited axial-force capacity of the vertical pipe when using compression fittings, the deteriorated hangars failed, shifting the load to the vertical pipe and couplings.
Figure 1 to the upper left is a view of a typical plumbing compression fitting used to splice plumbing pipes.
During scheduled services, give the fitting four or five pumps of grease.
The company said the fittings produced through the extrusion process were stronger and competitively priced.
The question, "as a complete beginner, do I really need a custom fitted set of clubs?" always crops up when talking about fittings. My answer to this is, "as a compete beginner, it would be best for you to have a course of lessons to get your setup correct".