ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00939.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00940.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

摘要:

AbstractWe present a simple form for the estimator of the point multiserial correlation coefficient between a quantitative variateXand a qualitative variate 7. Given a bivariate sample grouped in the form of anr×ccontingency table the estimator is based on finding the optimumY‐scores which maximize the correlation coefficient. The resulting estimator is equivalent to Das Gupta's (1960) for ungroupedX‐values, with the advantage of simplicity in its calculation. Under the assumption of conditional normality, the significance of point multiserial correlation may be studied by anF

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00941.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

摘要:

SummaryThe maximum possible autocorrelations, for moving average processes of orderq, have recently been discussed. In this paper, we give the corresponding process parameter values when greatest (or least) autocorrelations are attained. The attainment of an individual autocorrelation bound often does not fully define the process, and for such cases we also investigate the possible conditional bounds for the remaining autocorrelations.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00942.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

摘要:

SummaryThe largest value of the constant c for whichholds over the class of random variablesXwith non‐zero mean and finite second moment, isc=π.Let the random variable (r.v.)Xwith distribution functionF(·) have non‐zero mean and finite second moment. In studying a certain random walk problem (Daley, 1976) we sought a bound on the characteristic functionof the formfor some positive constant c. Of course the inequality is non‐trivial only provided that.This note establishes that the best possible constant c =π.The wider relevance of the result is we believe that it underlines the use of trigonometric inequalities in bounding the (modulus of a) c.f. (see e.g. the truncation inequalities in §12.4 of Loève (1963)). In the present case the bound thus obtained is the best possible bound, and is better than the bound(2) |1‐ϕ(θ)| ≥ |θEX|‐θ2EX2\2obtained by applying the triangular inequality to the relationwhich follows from a two‐fold integration by parts in the defining equation (*).The treatment of the counter‐example furnished below may also be of interest.To prove (1) withc=π, recall thatsin u>u(1‐u/π) (all realu), soSince |E sinθX|‐|E sin(‐θX)|, the modulus sign required in (1) can be inserted into (4).Observe that sincesin u>uforu0. Then (1) is equivalent to(6)c0 andEX2. Consider the r.v.where 0

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00943.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00944.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

摘要:

AbstractIf {Xn} is an irreducible aperiodic Markov chain on a state apacedenote the mean one step change of position, or “drift”, of {Xn} at j. The main result of this note is to show that, when |µ(j)| is bounded, {Xn} admits a stationary distribution {πj}if and only if for someN>0 and some state i, lim inf ∑when this holds, the limit infimum is in fact. Many of the known sufficient or necessary criteria for the existence of a stationary distribution can then be derived easily from this and related

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00945.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

摘要:

SummaryComputer simulation is employed to investigate the effects of quadrat size, sampling and estimation method, and cluster spread, density and size when estimating Neyman Type A and Thomas distributional parameters from quadrat samples. Results obtained indicate that quadrat size and cluster spread affect the estimates. Use of first order standard errors in selecting suitable quadrat sizes is discussed. Where clusters have non‐zero spread, the usual situation in practice, cluster density is generally overestimated and cluster size underestimated, which suggests the need for development of modified estimation procedure

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00946.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00947.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1975.tb00948.x

出版商:Blackwell Publishing Ltd    

年代:1975

数据来源: WILEY