Régime des chambres de commerce

An Introduction to the theory of statistics

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Monograph

Identifikator:: 834582015

URN:: urn:nbn:de:zbw-retromon-77707

Document type:: Monograph

Title:: Régime des chambres de commerce

Place of publication:: Paris

Publisher:: Libr.-impr. réunies

Year of publication:: 1894

Scope:: 1 Online-Ressource (390 S)

Collection:: Economics Books

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THEORY OF STATISTICS. expressed symbolically by expanding the ultimate in terms of the positive frequencies, and writing each such expansion not less than zero. We will consider the cases of one, two, and three attributes in turn. 8. If only one attribute be noted, say 4, the positive frequencies are V and (4). The ultimate frequencies are (4) and (a), where (a) = NN = (4). The conditions of consistence are therefore simply M40 N-(4)40 or, more conveniently expressed, (@ (A)<0 (5) (A): AE. (1) These conditions are obvious: the number of 4’s cannot be less than zero, nor exceed the whole number of observations. 9. If two attributes be noted there are four ultimate frequencies (4B), (4B), (aB), (eB). The following conditions are given by expanding each in terms of the frequencies of positive classes— (a) (4B)<0 or (45) would be negative (6) (AB) (4)+(B)-N ,, (af) ” ” (2) (c) (AB)}(4) » (45) ” ” ( (d) (4B)3(B) » (eB) ” ) (a), (c), and (d) are obvious; (b) is perhaps a little less obvious, and is occasionally forgotten. It is, however, of precisely the same type as the other three. None of these conditions are really of a new form, but may be derived at once from (1) (a) and (1) (6) by specifying the universe as B or as f respectively. The conditions (2) are therefore really covered by (1). 10. But a further point arises as regards such a system of limits as is given by (2). The conditions (a) and (b) give lower or minor limits to the value of (4B); (¢) and (d) give upper or major limits. If either major limit be less than either minor limit the conditions are impossible, and it is necessary to see whether (4) and (B) can take such values that this may be the case. Expressing the condition that the major limits must be not less than the minor, we have— (4)40 { (B)<0 } 4)» (B)»N These are simply the conditions of the form (1). If, therefore, (4) and (B) fulfil the conditions (1), the conditions (2) must be 20

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