摘要:

AbstractIn this article an attempt is made to prove that T1=ΠN+1i=1ysiiand T2=(X1+…+XN+1)s1+…+sN+1 are independently distributed whereX1,…, XN+1are generalized gamma variates, Yi=Xi./(X1+……+XN+1) ands1,…, sN+1are non‐negative integers. It is shown that when theXi's are certain two‐parameter gamma variablesT1andT2are independent and the independence does not hold good when the parameters are arbitrary. The density ofT1is also obtained in terms of H‐functions and M

ISSN:0319-5724    

DOI:10.2307/3314997.o

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThe object of this paper is to introduce certain properties of three new types of statistical distributions associated with generalized hypergeometric functions. The generalized phase and radial density functions associated with these distributions are obtained by making use of either characteristic functions or weighted‐mixture representations, where the independentxandycomponent distributions are not necessarily the same. 0nly bivariate situations are investigated explicitly. However, the results can be extended to multivariate cases by adopting a similar procedure. The results given recently by McNolty and Tomsky follow as special cases of the results of this pape

ISSN:0319-5724    

DOI:10.2307/3314998

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractIn this paper we study the distribution ofT= XS −11, whereXwith orderp × qis normally distributed with zero expectations and covariance matrix Σ⊗V, (that is,Cov( x−i, x−j) = σij, x−jbeing thej‐th column ofX, Σ=(σij)) and whereS1′S1=Sis distris uted as Wishart independently ofX, withd.f.=fand parameter matrix Σ=(σij) This is then a multivariate extension of the stu‐dentization process. As we shall see, however, the distribution ofTdepends on howSis partitioned. In this paper we shall consider the cases whereS1is lower triangular with positive diagonal elements and where S, is upper triangular with positive diagonal elements. The distributions ofTcorresponding to these two decompositions ofSare called respectively the upper and lower disguised matrix‐tdistributions. Properties of these distributions are derived. Some applications of these distributions to multivariate regressi

ISSN:0319-5724    

DOI:10.2307/3314999

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThis paper deals with the study of probability models for inter‐birth intervals. Expressions for the first four moments have been obtained under general probability distributions for the various components of the inter‐birth interval. The exact probability distribution of the inter‐birth interval has been obtained for a continuous

ISSN:0319-5724    

DOI:10.2307/3315000

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThere have been various attempts to use the Pearson type I curve for the purpose of graduating age‐specific fertility rates for human populations. This article attempts to broaden the scope of application of this curve, and discusses three particular areas where such application of this curve would be feasible. These areas are: simulation of age‐specific fertility rates; estimation of certain fertility parameters where statistics are either unreliable or incomplete as is the case in most developing countries; and projections of births. The writers feel that the greatest potential of the Pearsonian type I curve lies in the area of parametric model building for birth projections. One of the important prerequisites for a fruitful application in this area is simplification of procedures and reduction of a number of parameters needed to derive the Pearsonian type I curve. This article presents new methods for deriving this latter curve. The results of the proposed models are tested against data on age‐specific fertility rates for C

ISSN:0319-5724    

DOI:10.2307/3315001

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThis article deals with the application of a new graphical system, known as Graphical Rational Patterns (GRP), to geostatistical data. The first portion of the paper provides a brief review of the system for readers who are unfamiliar with it. This is followed by a series of annotated illustrations based on recent Canadian data. The paper emphasizes that the GRP system is particularly suitable for producing large numbers of inexpensive drafts or experimental maps by non‐cartographers; as such, the system contributes to geostatistical analysis undertaken by demographers, statisticians and others. An attempt is made to substantiate that the GRP system (i) introduces improved arrays of symbols (e.g., with regard to homogeneity and “rationality”); (ii) provides graphs and maps with improved “readability” and transmittance of general trends; (iii) suggests solutions where conventional methods are inapplicable or in

ISSN:0319-5724    

DOI:10.2307/3315002

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThroughout this note, (Xj) ∞1is a sequence of independent and identically distributed random variables, defined on a probability space (Ω, ℑ ρ) and having common distributionF.It is shown that if the cumulative distribution function (orcdf)Fis continuous, and F N*(x)=N−1Σ N1uN(x‐Xj) where (uN) ∞1is a sequence ofcdf's converging weakly to thecdfof the unit mass at zero, andF *Nalmost surely converges uniformly toF.This result implies that ifFhas a densityfand fNis a typical nonparametric density estimator and FN(x) = ∫ x−∞fN(t)dt then, with probability

ISSN:0319-5724    

DOI:10.2307/3315003

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractLetx' = (x1,…, xp) have a normal distribution with mean vector zero and covariance matrix Σ. Then Kshirsagar [(1961), (1966)] gives a criterion for testing the hypothesis that a single latent vector of Σ has a specified direction. Here we generalize Kshirsagar's results to the simultaneous testing of more than one vec

ISSN:0319-5724    

DOI:10.2307/3315004

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThis note tries to answer the complaint that the computer‐dealt hands, in bridge tournaments, seem to break too often in an unusual manner and that hand patterns are biased toward hands with long suits. Results of some empirical studies on computer‐dealt and man‐dealt hands are reported in this ar

ISSN:0319-5724    

DOI:10.2307/3315005

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractConsider a sample ofnobservations such that a single observation is randomly drawn from each ofnstrata, each having meanuiand variance σ2i(i=1,…,n). Two estimators for the variance of the sample mean are proposed and their relative efficiency is examin

ISSN:0319-5724    

DOI:10.2307/3315006

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY