An Introduction to the theory of statistics

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Monograph

Identifikator:: 876375174

URN:: urn:nbn:de:zbw-retromon-1989

Document type:: Monograph

Author:: Lilienthal, Johann

Title:: Fabrikorganisation, Fabrikbuchführung und Selbstkostenberechnung der Firma Ludw. Loewe & Co. Actiengesellschaft, Berlin

Place of publication:: Berlin

Publisher:: Verlag von Julius Springer

Year of publication:: 1907

Scope:: 1 Online-Ressource (XI, 220 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Die Geschäftsbuchführung.

Collection:: Economics Books

XV.—BINOMIAL DISTRIBUTION AND NORMAL CURVE. 315 Jour. Roy. Stat. Soc., vol. Ixxiii., 1910, p. 26. (A binomial distribu- tion with negative index, and the related curve, i.e. a special case of one of Pearson's curves, ref. 13.) The Resolution of a Distribution compounded of two Normal Curves into its Components. (18) PEARsoN, KARL,“ Contributions to the Mathematical Theory of Evolu- tion (on the Dissection of Asymmetrical Frequency Curves),” Phil. Trans. Roy. Soc., Series A, vol. clxxxv., 1894, PZ (19) Epceworrn, F. Y., “On the Representation of Statistics by Mathema- tical Formule,” part ii., Jour. Roy. Stat. Sec., vol. Ixii., 1899, p. 125. (20) PearsoN, KARL, “On some Applications of the Theory of Chance to Racial Differentiation,” Phil. Jay. 6th Series, vol. i., 1901, p. 110. (21) HELGUERO, FERNANDO DE, *‘ Per la risoluzione delle curve dimorfiche,” Biometrika, vol. iv., 1905, p. 230. Also memoir under the same title in the Transactions of the Reale Accademia dei Lincei, Rome, vol. vi., 1906. (The first is a short note, the second the full memoir, ) See also the memoir by Charlier, cited in (2), section vi. of that memoir dealing with the problem of dissection. Testing the Fit of an Observed to a Theoretical or another Observed Distribution. (22) PEARSON, KARL, “On the Criterion that a given System of Deviations from the Probable, in the Case of a Correlated System of Variables, is such that it can be reasonably supposed to have arisen from random sampling,” Phil. Mag., 5th Series, vol. 1., 1900, p- 157. (23) Pearson, KARL, “On the Probability that Two Independent Distribu- tions of Frequency are really Samples from the same Population,” Biometrika, vol. viil., 1911, p- 250 ; also Biometrika, vol. x., 1914, pp. 85-143, EXERCISES. 1. Calculate the theoretical distributions for the three experimental cases (1), (2), and (8) cited in § 7 of Chapter XIII. 2. Show that if np be a whole number, the mean of the binomial coincides with the greatest term. 3. Show that if two symmetrical binomial distributions of degree n (and of the same number of observations) are so superposed that the rth term of the one coincides with the (r+1)th term of the other, the distribution formed by adding superposed terms is a symmetrical binomial of degree n+ 1. [Note : it follows that if two normal distributions of the same area and standard-deviation are superposed so that the difference between the means is small compared with the standard-deviation, the compound curve is very nearly normal. ] 4. Culculate the ordinates of the binomial 1024 (05+ 05)", and compare them with those of the normal curve. 5. Draw a diagram showing the distribution of statures of Cambridge students (Chap. VI., Table VII), and a normal curve of the same area, mean, and standard-deviation superposed thereon. 6. Compare the values of the semi-interquartile range for the stature distributions of male adults in the United Kingdom and Cambridge students, (1) as found directly, (2) as calculated from the standard-deviation, on the assumption that the distribution is normal.

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