Studies in securities

Bibliographic data

Monograph

Identifikator:: 1757542078

URN:: urn:nbn:de:zbw-retromon-134903

Document type:: Monograph

Title:: Studies in securities

Edition:: Revised

Place of publication:: New York

Publisher:: Jas. J. Oliphant & Co.

Year of publication:: 1927

Scope:: 81 S.

Digitisation:: 2021

Collection:: Economics Books

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L—NOTATION AND TERMINOLOGY. 11 gate of frequencies of the second order, and the twelve classes of the second order which can be formed where three attributes have been noted may be grouped into three such aggregates. 12. Class-frequencies £ ay in tabulating, be arranged so that frequencies of the same order and frequencies belonging to the same aggregate are kept together. Thus the frequencies for the case of three attributes should be grouped as given below ; the whole number of observations denoted by the letter I being reckoned as a frequency of order zero, since no attributes are specified :— Order 0. WN Order 1. (4) (B) (7 (a) (B) i Order 2. (4B) (40) « 4p) (dy) (aB) (aC) | . () (a3) (a7) (, Order 3. (ABC) (a BC) (4By) (aBy) (ABC) (afC) (487) (apy) 13. In such a complete table for the case of three attributes, twenty-seven distinct frequencies are given :—1 of order zero, 6 of the first order, 12 of the second, and 8 of the third. It is, however, in no case necessary to give such a complete statement. The whole number of observations must clearly be equal to the number of 4’s together with the number of a’s, the number of 4’s to the number of 4’s that are B together with the number of 4’s that are not B ; and so on,—i.e. any class-frequency can always be expressed vn terms of class-frequencies of higher order. Thus— N=(4)+(a)=(B)+(B)=ete. = (LR) + (4B) + (aB) + (af3) = ete. @) (4)= (4B) + (48) = (40) + (47) =eto. | (4B) = (4BC) + (4 By) = ete. ) Hence, instead of enumerating all the frequencies as under (1), no more need be given, for the case of three attributes, than the eight frequencies of the third order. If four attributes had been noted it would be sufficient to give the sixteen frequencies of the fourth order. The classes specified by all the attributes noted in any case, t.e. classes of the nth order in the case of n attributes, may be

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