ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00541.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryA procedure is derived for estimating the distribution of diameters of spherical particles embedded in an opaque solid from a given grouped distribution of diameters of observed circles formed by their intersection with a random plane. The precision of the estimates can be characterized by the dispersion matrix of the joint estimates, which in its turn can also be estimated. Some numerical examples are given as well, one of them concerning the distribution of second‐phase spheroids in a sample of a high‐impact polystyr

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00542.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00543.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryThis report presents an approach to stochastic programming. It treats mainly the difficulties arising in formulating the problem and the possibilities to derive a deterministic problem by which it can be replaced. In a sense the approach of this report unifies different viewpoints on stochastic programming problems as they have been published in the literature.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00544.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryIn this paper the authors present the results of a sampling experiment to determine the power functions of the two‐sample rank tests of WILCOXON, VAN DER WAERDEN and TERRY against shift alternatives for normal parent distributions, based on 2000 trials for each alternative. The sample sizes considered are m = n = 6 and m = n = 10. The powers of the three rank tests are compared with the power of the STUDENT t‐test and with each other. The results indicate that in small samples (i) the power of the WILCOXON test is not much smaller than the power of the t‐test and (ii) the normal scores tests are only slightly superior to the WILCOXON test, if a

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00545.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00546.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryLet X and Y be random variables with distribution functions F and G and medians ζand η, respectively. X will be said to be more dispersed about the median than Y if F(x+ζ) – F(–x+ζ) G (x+η) – G (–x+η)for allx>O, with sharp inequality holding for some positivex. Asymptotically nonparametric tests for the hypothesis that F (x+ζ) = G (x+η) against alternatives of the above type (for ζ and η unknown), provided F(x+ζ) (but not necessarily G (x+η)) is symmetric and Fand G have bounded densities, are constructed from a subclass Of SUKHATME'S modified generalized U ‐ statistics [12]. One simple test of this subclass turns out to be the MANN‐WHITNEY test as performed on the |Xi–ζ| and | Yj–η| where ζ and η are the corresponding sample medians. Consistency and PITMAN efficiencies of some of the tests proposed are discussed under two families of alternatives in which the Y's differ from the X's through departure from symmetry as well as by being more (less) dispersed: a model of “heterogeneous response” and the wellknown gross error model. The usual scale alternatives are also studied and the relationship of our tests to those previously giv

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00547.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00548.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00549.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00550.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY