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Volume 10 - September 1973

Contents

Page 6 of 6

Front Matter

Short Communications

  • A note on Kendall's autoregressive series

  • T. J. Brown, J. C. Hardin
  • Published online by Cambridge University Press:
    14 July 2016, pp. 475-478

  • Realizations of the autoregressive series considered by Kendall are generated using both Gaussian and uniformly distributed random variables. Estimates of the autocorrelation and power spectrum of the process obtained from these realizations are compared with the theoretical expressions derived by Bartlett. Agreement is well within the theoretical variance.

Other

Back matter

  • JPR volume 10 issue 3 Cover and Back matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. b1-b6
    • Article
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Short Communications

  • A more general form of a theorem of Crofton

  • H. Ruben, W. J. Reed
  • Published online by Cambridge University Press:
    14 July 2016, pp. 479-482

  • Let Dj be a domain in nj,-dimensional Euclidean space, for j = 1, …, k. Suppose that for each j = 1,…, k, Nj points are chosen independently at random in Dj. A theorem, which is an extension of a theorem of Crofton, is proved about the expected value of functions of the points.

Front Matter

Back Matter

Short Communications

  • The random volume of interpenetrating spheres in space

  • P. A. P. Moran
  • Published online by Cambridge University Press:
    14 July 2016, pp. 483-490

  • The distribution of the volume occupied by random spheres in a cube is considered, both when the number of spheres is fixed and when their centres form a Poisson field. The mean and variance are obtained and in the latter case the distribution is proved to converge to normality. The probability of complete coverage is also obtained heuristically.

Front Matter

Back Matter

Page 6 of 6