Journal of the Royal Statistical Society Series B (Statistical Methodology)

Neyman, Jerzy; Scott, Elizabeth L.

doi: 10.1111/j.2517-6161.1958.tb00272.xpmid: N/A

The basic hypothesis underlying current deterministic cosmologies, namely the so‐called cosmological principle, can be stated precisely only in terms of probabilistic concepts. Consequently, considerable progress and aesthetic gain may be expected if determinism is abandoned and replaced by a frank probabilistic treatment of cosmology. This requires the adoption of the view that the Universe is a realization of a stochastic process which is stationary in the three (spatial) co‐ordinates (cosmological principle) and possibly also stationary in the fourth (time) co‐ordinate (“perfect” cosmological principle). Two examples are given of problems relevant to deterministic cosmological theories that elude deterministic treatment, but lend themselves to an indeterministic statistical study.

doi: 10.1111/j.2517-6161.1958.tb00273.xpmid: N/A

Watson, G. S.

doi: 10.1111/j.2517-6161.1958.tb00274.xpmid: N/A

Suppose that in a chi‐squared goodness‐of‐fit test the unknown parameters are estimated from the likelihood of the continuous observations before grouping. The effect on the distribution of the test criterion is examined.

doi: 10.1111/j.2517-6161.1958.tb00275.xpmid: N/A

Barton, D. E.

doi: 10.1111/j.2517-6161.1958.tb00276.xpmid: N/A

(1) The Matching Problem is reviewed. (2) Stevens's approach is generalized to yield the explicit results so far known. (3) A continuous range of Poisson limits is derived for the various matching distributions by an elementary method (alternative to Kaplansky's symbolic proof). (4) The approximations afforded by some of these are improved by orthogonal polynomial fitting. (5) Further Poisson limits are derived for certain general classes of multiple matching distributions; the asymptotic form for the number of Latin Rectangles is derived as a corollary and some numerical comparisons made. (6) Levene's matching problem is generalized: A general Poisson limit is obtained and some exact distributions derived. Kullback's matching distribution is generalized and a general Poisson limit obtained.

Silvey, S. D.

doi: 10.1111/j.2517-6161.1958.tb00277.xpmid: N/A

The Lindisfarne scribes' problem is one of estimating, from observations on an ordered set of random variables, the number of changes which occur in the distribution functions of these random variables as they are considered in order. This is a multiple decision situation and it is suggested that, in the absence of a loss function, the principle of controlling the probability of over‐estimating the number of changes, which is a natural extension of the principle underlying many currently applied tests of significance, might be used. An estimation procedure, based on this principle, is suggested for the Lindisfarne scribes' problem, and some of its implications are discussed.

Lindley, D. V.

doi: 10.1111/j.2517-6161.1958.tb00278.xpmid: N/A

x is a one‐dimensional random variable whose distribution depends on a single parameter θ. It is the purpose of this note to establish two results:

Banerjee, D. P.

doi: 10.1111/j.2517-6161.1958.tb00279.xpmid: N/A

By rearranging the factors of the complicated rth moment of the distribution of a statistic in multivariate analysis and using Mellin's Transformation it is possible to find the exact distribution of the statistic. This cannot be found easily by other methods.

Broadbent, S. R.

doi: 10.1111/j.2517-6161.1958.tb00280.xpmid: N/A

The output of a Markov process producing good and bad items in sequence is inspected for the bad items. A measure is proposed of the work involved, and the estimation required for this measurement is discussed.

Davies, Hilda M.; Jowett, G. H.

doi: 10.1111/j.2517-6161.1958.tb00281.xpmid: N/A

The generalized least squares method is used to establish a practical method of fitting the function θ(1 — ρ|τ|) to the first few serial variation statistics of a time series for use as an approximation to the beginning of a serial variation function of more general type. A large‐sample goodness of fit test is given, and also a method of testing the goodness of fit of a common or specified function, or functions with a common or specified value of ρ, to several series.