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SummaryExtrapolation of time‐series.In this paper only singular stationary stochastic processes are considered, which means that the error variance in predicting the future may be made indefinitely small. From the point of view of the spectral distribution function there are various types of singular processes. Likewise a classification of singular processes may be made by the form of the prediction formula and by the way the prediction error tends to zero. An attempt to find a correspondence between these classifications is made.

SummaryThe effective size of stratified samples.In this paper, the notion of effective size of a stratified sample is introduced, being defined as the total size of a stratified sample with optimum allocation over the strata that yields an estimate with the same sampling error as the sample concerned. The efficiency is defined as the ratio between the effective sample size and the actual size of the sample. This efficiency is rather low if allocation deviates considerably from the optimum.Furthermore we define the marginal rate of return by the increase in effective sample size divided by the increase in sample size in one or some of the strata in an optimally allocated stratified sample. Finally the substitution rate of return indicates by how many elements the sample size in the remaining strata can be reduced if the effective sample size is to remain unchanged. A practical example is afforded in which the variances in the strata are assumed equal.

SummaryA sample estimate of the poultry distributionIn 1954 a sample survey was carried out of the returns of the agricultural census, May 1954, in order to establish the distribution of the number of holdings and the number of poultry, by size‐group of arable land and by size‐group of number of poultry. A simple 10 per cent, sample was planned and the expected variances of the numbers of poultry in each size‐group were estimated beforehand. The method of estimation is indicated in this paper. This resulted in comparatively high relative errors in the size‐groups above 500 hens and also in the size‐groups of arable land. Therefore holdings with 500 hens and over were enumerated completely. Some tests were performed with the sample results and finally the efficiency of the stratification is discussed.