cumulativeadj.

/ˈkjuːmjʊlətɪv/

Etymology: < Latin cumulāt-, participial stem of cumulāre (see cumulate adj.) + -ive suffix. Compare modern French cumulatif, -ive.

†1. Such as is formed by accumulation or heaping on (as opposed to organic growth). Obsolete.

ΚΠ

1605 F. Bacon Of Aduancem. Learning ii. sig. Ee4 As for knowledge which Man receiueth by teaching, it is Cumulatiue and not Originall, as in a water, that besides his own spring-heade is fedde with other Springs and Streames.

a. Constituted by or arising from accumulation, or the accession of successive portions or particulars; acquiring or increasing in force or cogency by successive additions, as cumulative argument, cumulative evidence, cumulative force.

ΚΠ

1668 Liberty of Conscience the Magistrates Interest 4 He..has not only the common tye of a Subject upon him, for his protection as a man, but the cumulative obligation, and thanks to pay for his Indulgence.

a1676 M. Hale Historia Placitorum Coronæ xiv. (T.) Among many cumulative treasons charged upon the late earl of Strafford.

1823 J. Keble Serm. (1848) ii. 37 The argument from the authority of implicit believers is cumulative: i.e. a fresh argument is added every time a new instance is observed of a man's finding his happiness in Christianity.

1841 R. W. Emerson Self-reliance in Ess. 1st Ser. (London ed.) 60 Always scorn appearances, and you always may. The force of character is cumulative.

1849 R. I. Murchison Siluria xx. 500 We have..cumulative evidence to prove the wide-spread diffusion of the same types.

1868 E. A. Freeman Hist. Norman Conquest (1876) II. ix. 432 There are several circumstances which have together a kind of cumulative force.

b. cumulative medicine n.

ΚΠ

1876 W. Begbie Bk. Med. Information App. 251 Digitalis is what is called a cumulative medicine: its effects are sometimes not immediately produced; but each successive dose remaining in the system, these may be seen even after the medicine is discontinued.

c. cumulative error n.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > result of > error in

error1715

riska1832

cumulative error1887

1887 Encycl. Brit. XXII. 707/2 [Surveying.] Cumulative error, not eliminable by circuiting, may be caused when there is much northing or southing..in the direction of the line.

1920 W. N. Thomas Surveying 509 Cumulative errors are those which tend always in the same direction, i.e. either to make the apparent measurements always too large or always too small... Cumulative errors are directly proportional to the number of observations.

1957 M. G. Kendall & W. R. Buckland Dict. Statist. Terms 74 Cumulative error, an error which, in the course of the cumulation of a set of observations, does not tend to zero.

3. Scots Law. Of jurisdiction: Concurrent, as opposed to privative or exclusive.

ΚΠ

1746–7 Act 20 Geo. II c. 43 §27 The jurisdiction hereby reserved to such Corporation..shall be..taken to be cumulative only.

1754 J. Erskine Princ. Law Scotl. I. i. ii. §6 Jurisdiction is either privative or cumulative..Cumulative, otherwise called concurrent, is that which may be exercised by any of two or more courts in the same cause.

4. That tends to accumulate.

ΚΠ

1873 H. Spencer Study Sociol. xiii. 324 Certain actions which go on in the first are cumulative, instead of being, as in the second dissipative.

5. cumulative vote n. a system of voting, where there are several representatives, in which each voter has as many votes as there are representatives, and may accumulate them upon one candidate or distribute them over any number of candidates; a system introduced in connection with the School Board elections in Great Britain.

ΘΚΠ

society > authority > office > appointment to office > choosing or fact of being chosen for office > election of representative body by vote > right to vote at elections > [noun] > systems of voting

scrutin de liste1851

cumulative vote1853

Australian ballot1888

preference1900

alternative vote1908

list system1908

preference voting1908

scrutin d'arrondissement1921

list voting1954

AV1965

1853 J. S. Mill Lett. (1910) I. 173 One very strong recommendation of the plan of cumulative votes occurs to me.

1880 J. McCarthy Hist. our Own Times IV. lix. 294 The School Boards..the principle of the cumulative vote was tested for the first time in their elections.

1886 J. Morley W. R. Greg in Crit. Misc. III. 255 Lord Grey's prescription..consisted of the following ingredients:—the cumulative vote; not fewer than three seats to each constituency, etc.

Draft additions 1993

a. Also, cumulative effect.

ΘΚΠ

the world > existence and causation > causation > effect, result, or consequence > [noun] > cumulative or ripple effect

ripple1838

cumulative effect1856

ripple effect1892

1856 Trans. Amer. Med. Assoc. 9 761 It was denied for years that strychnia could exhibit any cumulative effects on the animal system.

1914 A. S. Blumgarten Materia Medica for Nurses v. 67 The effects produced by the amount of drug which accumulates in the body, are called cumulative effects.

1981 R. Hayman Kafka vii. 91 The cumulative effect of working six hours a day for six days a week.

b. Mathematics. Designating a probability distribution which is the integral up to a particular value of a probability density function, and therefore represents the probability that this value is not exceeded by a random variable with this distribution.

ΘΚΠ

the world > relative properties > number > probability or statistics > [adjective] > relating to distribution

multinomial1608

Poisson1839

Poissonian1894

cumulative1950

Weibull1955

1950 W. Feller Introd. Probability Theory & its Applic. I. vii. 133 The term distribution function is used in the mathematical literature for any never-decreasing function F(x) which tends to 0 as x → −∞, and to 1 as x → ∞. Statisticians currently prefer the term cumulative distribution function, but the adjective ‘cumulative’ is redundant.

1962 D. R. Cox Renewal Theory i. 3 The distribution of X is determined by the p.d.f., f(x), but it is for some purposes convenient to work with other functions equivalent to f(x). One such is the cumulative distribution function, F(x), giving the probability that a component has failed by time x.

1976 Biometrika 63 436 Let G(λ) be the empirical cumulative distribution function of the numbers λ₁,.., λ_s.

Draft additions September 2016

cumulative sum n. (a) the aggregate or total amount of something, the sum total; (b) Mathematics a partial sum of terms of a given sequence.

ΚΠ

1853 Morning Post 18 Aug. 2/2 The cases in which the payment of the penny is made in separate and isolated, instead of cumulative sums, present greater difficulty.

1928 Jrnl. Amer. Statist. Assoc. 23 123 The movement of the cumulative sum of the xy products shows the trend in the degree of concurrence.

1956 Times 7 Dec. 9/5 Britain had already made available a cumulative sum of about £86m. in grants since 1951.

1995 Jrnl. Appl. Econometrics 10 105 Table II presents the Phillips–Ouliaris bounds tests for convergence and the cumulative sums of the eigenvalues.

2012 Oecologia 168 705/1 The thermal sum is the cumulative sum of daily mean temperatures exceeding +5°C from the beginning of March.

This entry has not yet been fully updated (first published 1893; most recently modified version published online March 2019).

单词	cumulative
释义	cumulativeadj. /ˈkjuːmjʊlətɪv/ Etymology: < Latin cumulāt-, participial stem of cumulāre (see cumulate adj.) + -ive suffix. Compare modern French cumulatif, -ive. †1. Such as is formed by accumulation or heaping on (as opposed to organic growth). Obsolete. ΚΠ 1605 F. Bacon Of Aduancem. Learning ii. sig. Ee4 As for knowledge which Man receiueth by teaching, it is Cumulatiue and not Originall, as in a water, that besides his own spring-heade is fedde with other Springs and Streames. View more context for this quotation 2. a. Constituted by or arising from accumulation, or the accession of successive portions or particulars; acquiring or increasing in force or cogency by successive additions, as cumulative argument, cumulative evidence, cumulative force. ΚΠ 1668 Liberty of Conscience the Magistrates Interest 4 He..has not only the common tye of a Subject upon him, for his protection as a man, but the cumulative obligation, and thanks to pay for his Indulgence. a1676 M. Hale Historia Placitorum Coronæ xiv. (T.) Among many cumulative treasons charged upon the late earl of Strafford. 1823 J. Keble Serm. (1848) ii. 37 The argument from the authority of implicit believers is cumulative: i.e. a fresh argument is added every time a new instance is observed of a man's finding his happiness in Christianity. 1841 R. W. Emerson Self-reliance in Ess. 1st Ser. (London ed.) 60 Always scorn appearances, and you always may. The force of character is cumulative. 1849 R. I. Murchison Siluria xx. 500 We have..cumulative evidence to prove the wide-spread diffusion of the same types. 1868 E. A. Freeman Hist. Norman Conquest (1876) II. ix. 432 There are several circumstances which have together a kind of cumulative force. b. cumulative medicine n. ΚΠ 1876 W. Begbie Bk. Med. Information App. 251 Digitalis is what is called a cumulative medicine: its effects are sometimes not immediately produced; but each successive dose remaining in the system, these may be seen even after the medicine is discontinued. c. cumulative error n. ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > result of > error in error1715 riska1832 cumulative error1887 1887 Encycl. Brit. XXII. 707/2 [Surveying.] Cumulative error, not eliminable by circuiting, may be caused when there is much northing or southing..in the direction of the line. 1920 W. N. Thomas Surveying 509 Cumulative errors are those which tend always in the same direction, i.e. either to make the apparent measurements always too large or always too small... Cumulative errors are directly proportional to the number of observations. 1957 M. G. Kendall & W. R. Buckland Dict. Statist. Terms 74 Cumulative error, an error which, in the course of the cumulation of a set of observations, does not tend to zero. 3. Scots Law. Of jurisdiction: Concurrent, as opposed to privative or exclusive. ΚΠ 1746–7 Act 20 Geo. II c. 43 §27 The jurisdiction hereby reserved to such Corporation..shall be..taken to be cumulative only. 1754 J. Erskine Princ. Law Scotl. I. i. ii. §6 Jurisdiction is either privative or cumulative..Cumulative, otherwise called concurrent, is that which may be exercised by any of two or more courts in the same cause. 4. That tends to accumulate. ΚΠ 1873 H. Spencer Study Sociol. xiii. 324 Certain actions which go on in the first are cumulative, instead of being, as in the second dissipative. 5. cumulative vote n. a system of voting, where there are several representatives, in which each voter has as many votes as there are representatives, and may accumulate them upon one candidate or distribute them over any number of candidates; a system introduced in connection with the School Board elections in Great Britain. ΘΚΠ society > authority > office > appointment to office > choosing or fact of being chosen for office > election of representative body by vote > right to vote at elections > [noun] > systems of voting scrutin de liste1851 cumulative vote1853 Australian ballot1888 preference1900 alternative vote1908 list system1908 preference voting1908 scrutin d'arrondissement1921 list voting1954 AV1965 1853 J. S. Mill Lett. (1910) I. 173 One very strong recommendation of the plan of cumulative votes occurs to me. 1880 J. McCarthy Hist. our Own Times IV. lix. 294 The School Boards..the principle of the cumulative vote was tested for the first time in their elections. 1886 J. Morley W. R. Greg in Crit. Misc. III. 255 Lord Grey's prescription..consisted of the following ingredients:—the cumulative vote; not fewer than three seats to each constituency, etc. Draft additions 1993 a. Also, cumulative effect. ΘΚΠ the world > existence and causation > causation > effect, result, or consequence > [noun] > cumulative or ripple effect ripple1838 cumulative effect1856 ripple effect1892 1856 Trans. Amer. Med. Assoc. 9 761 It was denied for years that strychnia could exhibit any cumulative effects on the animal system. 1914 A. S. Blumgarten Materia Medica for Nurses v. 67 The effects produced by the amount of drug which accumulates in the body, are called cumulative effects. 1981 R. Hayman Kafka vii. 91 The cumulative effect of working six hours a day for six days a week. b. Mathematics. Designating a probability distribution which is the integral up to a particular value of a probability density function, and therefore represents the probability that this value is not exceeded by a random variable with this distribution. ΘΚΠ the world > relative properties > number > probability or statistics > [adjective] > relating to distribution multinomial1608 Poisson1839 Poissonian1894 cumulative1950 Weibull1955 1950 W. Feller Introd. Probability Theory & its Applic. I. vii. 133 The term distribution function is used in the mathematical literature for any never-decreasing function F(x) which tends to 0 as x → −∞, and to 1 as x → ∞. Statisticians currently prefer the term cumulative distribution function, but the adjective ‘cumulative’ is redundant. 1962 D. R. Cox Renewal Theory i. 3 The distribution of X is determined by the p.d.f., f(x), but it is for some purposes convenient to work with other functions equivalent to f(x). One such is the cumulative distribution function, F(x), giving the probability that a component has failed by time x. 1976 Biometrika 63 436 Let G(λ) be the empirical cumulative distribution function of the numbers λ₁,.., λ_s. Draft additions September 2016 cumulative sum n. (a) the aggregate or total amount of something, the sum total; (b) Mathematics a partial sum of terms of a given sequence. ΚΠ 1853 Morning Post 18 Aug. 2/2 The cases in which the payment of the penny is made in separate and isolated, instead of cumulative sums, present greater difficulty. 1928 Jrnl. Amer. Statist. Assoc. 23 123 The movement of the cumulative sum of the xy products shows the trend in the degree of concurrence. 1956 Times 7 Dec. 9/5 Britain had already made available a cumulative sum of about £86m. in grants since 1951. 1995 Jrnl. Appl. Econometrics 10 105 Table II presents the Phillips–Ouliaris bounds tests for convergence and the cumulative sums of the eigenvalues. 2012 Oecologia 168 705/1 The thermal sum is the cumulative sum of daily mean temperatures exceeding +5°C from the beginning of March. This entry has not yet been fully updated (first published 1893; most recently modified version published online March 2019). < adj.1605
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