摘要:

In discrete distributions, it has often been recommended that an auxiliary random experiment should be carried out so as to make the size of the test equal to the significance level. In certain experimental situations, this procedure would be time-consuming and even embarrassing to the statistician. An alternative criterion of significance is suggested, the mid or median probability. To avoid computationsP(χ), the probability of the square root of a chi-square variable, can be used in the binomial, Poisson and hypergeometric distributions as an approximation to the mid probability. In statistical control of counting experiments or where experiments are being repeatedP(χ) rather thanP(χc), the probability of χ corrected for continuity, gives acceptable approximations to size of significance levels. Some computations are given for the multinomial distribution which show that hereP(χ2) gives acceptable approximations.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482105

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

A multiple regression model based on the Poisson density is discussed. Point estimation by maximum likelihood results in estimating equations which can be solved by iteration based on scoring or on a successively revised weighted least squares estimator. The first round of each iterative process is shown to be BAN, provided that the ordinary least squares estimator is used as the initial condition. A minimum chi-squared estimator, which can be computed directly from sample observations, is derived and shown to be BAN. A consistent estimator of the variance-covariance matrix for each estimation procedure is given.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482106

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

A standard practice of physical scientists is to report estimates (“measurements”) accompanied by their standard errors (or alternatively “average errors” or “probable errors”). Such reports are interpreted flexibly as appropriate in various contexts of application. With the usual normality assumption, such reports may be read as representing confidence intervals or limits at the various confidence levels, and this omnibus character largely accounts for the convenience and flexibility of such reports and interpretations. For estimators not normally distributed, a formal analogue of such reports is provided byconfidence curves, which are estimates of an omnibus form incorporating confidence intervals and limits at various levels. The definition and computation of such estimates, and their graphical representation and interpretation, are discussed and illustrated by an example.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482107

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Changes in the distribution of individuals' dividend income by income group afford a measure of changes in the distribution of individually owned stock by income group. Between 1917 and 1957 the share of individuals' dividend income going to persons in the top percentile of the income distribution has halved, while the share going to persons in the upper five percentiles has fallen by one-third. The decline has been irregular, about half of it occurring in the periods 1927–1931 and 1937–1943. This evidence of change in the distribution of individually owned stock by income group contrasts with evidence which suggests an absence of change in the distribution by wealth group.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482108

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The problem is the determination of an optimal selection method of quasi-range for setting one-sided confidence bounds and confidence intervals for the standard deviation from a given distribution. The proposed methods of optimal selection are applied to random ordered samples from the normal, exponential and rectangular distributions. Tables of confidence bounds for the standard deviation of these distributions are given for confidence levels commonly used in statistical work. These are compared with the results of standard procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482109

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482110

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The problem discussed arises in situations where one wishes to choose weights which minimise the deviation of the weighted sum ofndistributions on the interval (O, L) from their lineal average. It is assumed the distributions differ only in their means which are evenly spaced over (O, L), thatnRis not less thanLwhereRis the length of the range of each distribution and that each point in (O, L) is covered by at most two of the ranges. A general solution is found from which it follows that the minimising weights are positive and obey certain inequalities. A table of results is given for the case where each distribution is a truncated normal distribution. The general problem is introduced by considering the practical question of how to obtain an even linear spread of spray.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482111

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The exact distribution of the Wilcoxon statistic was calculated for five specific cases where both samples contained five observations, some of which were tied. The five specific cases were obtained from an actual experiment. The exact distributions for each of these five cases are compared with some approximations at points near 1, 5, and 10 per cent. Critical values and associated probabilities have been calculated for the exact and approximate distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482112

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

A random experiment which results in some ordering of theMeventsE1,E2, ···,EMmay be such that these events are observable not individually, but in the form of ordered subsets. A discussion is given for the partial order problem of determining information about one or more complete orders of theMevents from partially ordered observations. Relationships are mentioned between the (rank-order) methods of the present paper and those of Rank Correlation and thek-sample problem.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482113

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Two groups,N1= α1+b1andN2= α2+b2, are compared in terms of their respective morbidity rates,p1andp2, in the presence of errors of misclassification (α1and α2are sure components;b1andb2are potential error terms). The four extreme situations for the compositions ofN1andN2are considered. Ratep1is assumed to apply to α1andb1;p2is assumed to apply to α1andb2. If there is a difference in rates for the error-free situation, then the observed difference is smaller in each of the error situations. Further, measurement errors reduce the chance of detecting a real difference.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10482114

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor