Download PDF by R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy: Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary

By R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy Neyman, Lucien M. Le Cam (eds.)

ISBN-10: 3642494668

ISBN-13: 9783642494666

ISBN-10: 3642497497

ISBN-13: 9783642497490

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Additional info for Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963

Sample text

18) 1 d A=---. 2 nUl dU l Now we must distinguish two cases according to the parity of n. Case 1. n even: n = 2 m. rs [(I) (e)] = Am-l [lP (u1 )] . r'J, [(I) (e)] = 2j u, (lIP ((l) d(l . P(e)=-- n Case 2. r1 [(I) (e)] = (I) Q d dUt 1 )] du l~. 21) . 22) + 1. 23) solve our problem for an arbitrary value of n. Let us now consider some particular cases. Particular cases. a) n = 2. 24) Q This formula was used by B. PICINBONO [2] and M. SAVELLI [3] and applied to the study of the granularity of photographic films.

21) . 22) + 1. 23) solve our problem for an arbitrary value of n. Let us now consider some particular cases. Particular cases. a) n = 2. 24) Q This formula was used by B. PICINBONO [2] and M. SAVELLI [3] and applied to the study of the granularity of photographic films. b) n = 3. 25) Remarks. 1. (/J (e) is surely nonnegative. 25), ep (u1) is certainly a nonincreasing function of I U 1 I. This result is strongly connected with the fact that n = 3. This can easily be seen. Due to isotropy, we can consider the spectral distribution of the weights dF (v) to be constituted by concentric spheres, each of uniform density.

D'ALEMBERT'S wrath overflowed when LAPLACE presented a paper on the tides to the Academy in 1777 without giving him what he considered enough acknowledgement and both he and LAPLACE wrote to LAGRANGE complaining each of the other's conduct. LEGENDRE was also unhappy about LAPLACE'S ambience. LEGENDRE read a paper to the Academy in 1784 (and printed in 1787) introducing his polynomials, in the course of solving the problem of the shape of the surface formed by the rotation of a homogeneous fluid.

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Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963 by R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy Neyman, Lucien M. Le Cam (eds.)


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