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maximum|ˈmæksɪməm|
Pl. maxima, rarely -ums.
[a. L. maximum, neut. of maximus, superl. of magnus great. Cf. F. maximum.]
1. Math. The greatest of all the values of which a variable or a function is capable; the value of a continuously varying quantity at the point at which it ceases to increase and begins to decrease.
1743Emerson Fluxions 104 In Case it..passes through one or more Maximums or Minimums; then the several Parts of the Fluent, between any given Point and each Maximum or Minimum must be separately found by distinct Operations. 1806Hutton Course Math. II. 306 If we would find the quantity ax-x2 a maximum or minimum; make its fluxion equal to nothing. 1856Sabine in Phil. Trans. CXLVI. 505 The declination has two easterly and two westerly maxima in the interval between two successive passages of the moon over the astronomical meridian.
2. gen. The highest attainable magnitude or quantity (of something); a superior limit of magnitude or quantity.
1740Cheyne Regimen 306 In the Works of the God of Nature, there is no Maximum or Minimum assignable, or conceiveable by us. 1755Winthrop Earthquakes 28 Laws of this sort are sufficiently vindicated..if upon the whole they produce a maximum of good. 1806Colquhoun Indigence 49 The art of conducting a nation to the maximum of happiness and the minimum of misery. 1855Bain Senses & Int. ii. ii. §14 (1864) 137 The animal powers attain their maximum in cold climates. 1902T. M. Lindsay Ch. & Ministry in Early Cent. vii. 279 A strange compound of minimum of fact and maximum of theory.
3. The highest amount (esp. of temperature, barometric pressure, etc.) attained or recorded within a specified period.
1850Edmonds in Rep. Brit. Assoc., Sections (1851) 32 The following remarkable maxima of temperature. 1860Maury Phys. Geog. Sea (Low) vii. §348 The barometer also has its maxima and minima readings for the day. 1880Daily News 18 Sept. 3/7 The maxima to-day were below 60 deg. in the Shetlands and Hebrides. 1902Westm. Gaz. 16 June 5/2 The years of sunspot maximum.
4. A superior limit imposed by authority; esp. in French Hist., a limit of price for corn.
1821Syd. Smith Wks. (1859) I. 352/1 The danger of insurrection is a circumstance worthy of the most serious consideration in discussing the propriety of a maximum. 1835Alison Hist. Europe (1847) IV. 164 They [the farmers, 1793] were compelled to part with their grain at the price fixed by the maximum, which was calculated on the scale of prices before the Revolution. 1941R. R. Palmer Twelve who Ruled x. 239 The Maximum of September 29 caused trouble from the start.
5. attrib.
a. quasi-adj. or adj., with the sense: That is a maximum, or that stands at the maximum; greatest. [Cf. F. la dépense maximum.]
1834M. Somerville Connex. Phys. Sci. xxvi. (1849) 297 Surround two poles of maximum cold. 1860Maury Phys. Geog. Sea (Low) ix. §430 The maximum density of average sea-water. 1861Times 23 July, The maximum contract price for the conveyance of these emigrants was 25l. 18s. 4d. per statute adult. 1879G. B. Prescott Sp. Telephone 96 A point of maximum disturbance. 1876Grant Burgh Sch. Scotl. ii. ii. 103 The heritors paying the maximum salary and the town paying {pstlg}12 annually for the support of a master. 1880C. R. Markham Peruv. Bark 405 The latter helping to produce a maximum temperature favourable to coffee cultivation.
b. Simple attributive: Pertaining to a maximum or maxima, as maximum period; maximum thermometer, a thermometer which records automatically the highest temperature within a given period. Also in Comb., as maximum-security (used attrib.).
1852Newton's Lond. Jrnl. Conjoined Ser. XLI. 402 An improved maximum thermometer. 1868Lockyer Elem. Astron. ii. (1879) 49 There is a minimum period, when none are seen for weeks together, and a maximum period, when more are seen than at any other time. 1966Punch 28 Dec. 962/2 The family wing of every prison enjoyed maximum security arrangements. 1969E. Ambler Intercom Conspiracy (1970) ii. 27 The special maximum-security passes that would be needed to gain admittance. 1972Guardian 29 Jan. 9/5 Albany, the new maximum security prison on the Isle of Wight.
Add:[5.] [b.] maximum likelihood Statistics, the highest value attained by a likelihood function as the population parameters vary; freq. used attrib. with reference to a method of estimating parameters by maximizing the likelihood or likelihood ratio.
1922R. A. Fisher in Phil. Trans. R. Soc. A. CCXXII. 323 For the solution of problems of estimation we require a method which for each particular problem will lead us automatically to the statistic by which the criterion of sufficiency is satisfied. Such a method is, I believe, provided by the Method of *Maximum Likelihood. 1937L. H. C. Tippett Methods of Statistics (ed. 2) iii. 95 The maximum likelihood estimate of σ is found to be the standard deviation. 1976Biometrika LXIII. 438 Table 3 shows the maximum likelihood fits, obtained by iterative search for various choices of x0. 1990Brain CXIII. 490 A cumulative Gaussian curve was fitted to each set of frequency-of-seeing data by a maximum-likelihood procedure.
Hence ˈmaximumly adv.
1949M. Mead Male & Female xiii. 275 Maximumly efficient and pleasant plumbing. 1981Christian Science Monitor 25 Feb. 21/2 Every door and window was maximumly secure. |