摘要:

Let R be the sample product-moment correlation coefficient computed from a random sample of n pairs of observations from a bivariate normal distribution with population correlation coefficient ρ. For −1 < r < 1, define fn(r,p) to be the density function for R, and Fn(r,p)=Pr[R <=r] to be the cumulative distribution function. Extensive tables of fn(r,p) and Fn(r,p) are given by David (1954) . Tables of upper and lower confidence limits on p are given by Odeh and Owen (1980). The major purpose of this paper is to give extensive tables of the critical values of the Distribution of R. In particular we give values of ry=r(y,n,ρ) to 5 decimal places which satisfy Fn(ry,ρ)= y. Tables are given for values of ρ=0.0(0.10)0.90, 0.95; n = 4(1)30(2)40(5)50(10)100(20)200(100)1000; Y=0.25, 0.10, 0.05, 0.025, 0.01, 0.005;Y=0.75, 0.90, 0.95, 0.975, 0.99, 0.995. We also show how critical values for ρ < 0 can be obtained from the tables.

ISSN:0361-0918    

DOI:10.1080/03610918208812243

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Asymptotically optimal experimental designs for animal bio-assays conducted in order to estimate virtually safe levels of exposure to chemical carcinogens are derived under the one-hit model and the probit model with known slope parameter. For these two models, the optimal designs involve assigning all available animals to the dose levels corresponding to the 80% and 50% response rates respectively. In both cases, the optimal designs are highly robust in the sense that the loss in efficiency is minimal if the dose actually employed is at all close to the optimal dose. In addition, the bias, variance and mean square error of the maximum likelihood estimator of the safe level of exposure under these two models are computed and compared with those of the jackknife estimator as well as an alternative estimator with reduced bias proposed by Salama, Koch & Tolley 1978. Twelve different procedures for obtaining approximate lower confidence limits on the safe dose are also compared in terms of their actual coverage probabilities and their precision.

ISSN:0361-0918    

DOI:10.1080/03610918208812244

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

This paper provides a Monte Carlo study of approximating the non-central Wishart distribution by Central Wishart distribution by mean of 1. Multivariate Gram-Chalier expansion and 2. Laguerre polynomial expansion. For assessing the closeness of these approximations, 1,000 independent 2×2 non-central Wishart matrices are generated by computer. The numerical results indicate that the multivariate Gram-Chalier expansion provides a close approximation to the non-central Wishart distribution as long as the correlation coefficient is less than 0.8. Also, it appears that the Gram-Chalier expansion approximation is better than the Laguerre polynomial expansion approximation when the probability values are large.

ISSN:0361-0918    

DOI:10.1080/03610918208812245

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Let X1,…,X2,…,XNbe multinomial with zero means, unitvariances, and equal correlations ρ>0. For i=l,…,N let Yi=|Xi| and let Y(1)&…&Y(N)denote the ordered Y's. Denote by FN(y;ρ) the probability that YN&y. In this paper tables of upper 100apercentage points of the distribution of YNare given. Values of ya=y(a,N,p)are given which satisfy FN(ya;ρ)=l−α for a=0.25, 0.10, 0.05, 0.025, 0.01, 0.005, 0.001; N=2(1)40(2)50; and p=0.100, 0.125, 0.200, 0.250, 0.300, 1/3, 0.375, 0.400, 0.500, 0.600, 0.625, 2/3, 0.700, 0.750, 0.800, 0.875, 0.900,1/(1+√N).

ISSN:0361-0918    

DOI:10.1080/03610918208812246

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

The LPnorm provides alternatives to least squares for estimating the coefficients of a linear regression model. Monte Carlo studies were performed using six different values of p (including the least squares case of p =2) and were compared by means of the relative efficiencies based on the generalised variances. Values of p other than 2 showed improvement over least squares for all non-normal error distributions. A rule for determining a suitable p on the basis of the kurtosis of the error distribution is proposed.

ISSN:0361-0918    

DOI:10.1080/03610918208812247

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

An algorithm for computing covariance and correlation matrices from data with missing values is presented. In terms of the number of operations performed (hence CPU time used) this algorithm is more efficient than that used by most statistical computing packages. CPU time efficiency is attained without undue increase in the number of input/output operations or memory space requirements.

ISSN:0361-0918    

DOI:10.1080/03610918208812248

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610918208812242

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor