Mathematical Statistics

PARTS III. and IV. of the twelfth volume of “Biometrika” contain papers of interest to all classes of statistician. Those especially attracted by work on the general mathematical theory of probability will welcome the continuation of Prof. Tchou-proff's paper on the “Expectation of the Moments of Frequency Distributions.” It will be agreed that the notation of mathematical expectation offers certain advantages over the iforms of expression more commonlv adopted in this; country, but Prof. Pearson does well to point out that the supposed fundamental distinction of method claimed by some Continental writers is nonexistent. He himself contributes a very interesting paper on. a method of generalising Tchebycheff's first theorem. He finds that the method of approximating to the limits of a probability is unlikely-to be of much practical value in the classes of function of usual occurrence. This result does not, of course, deprive Tchebycheff's work of its interest in permitting of the establishment of Bernoulli's theorem and of Poisson's generalisation of that theorem by elementary methods. Paper's of importance both to the student of theoretical -statistics and to the practical computer are those of Miss Pairman and Prof. Pearson on the correction of the moment coefficients in limited range frequency distributions, of “Student” on-deviations from the Poisson limit to the binomial in actual data, and an editorial,. entitled “Peceavimus,” correcting errors in various published formulae.