摘要:

LetX= (X1,…, Xk)’ be a k-variate (k ≥ 2) normal random vector with unknown population mean vectorμ= (μ1,…, μk)’ and covariance matrix Σ of order k and let μ[1]≤ … ≤ μ[k]be the ordered values of the μ ’ s. No prior knowledge of the pairing of the μ[i]with the Xj. (or μ[i]with the σj2) is assumed for any i and j (1 ≤ i, j ≤ k). Based on a random sample of N independent vector observations onX, this paper considers both upper and lower (one-sided) and two-sided 100γ% (0 < γ < 1) confidence intervals for μ[k]and μ[1], the largest and the smallest mean, respectively, when Σ is known and when Σ is equal to σ2R with common unknown variance σ2> 0 and correlation matrix R known, respectively. An optimum two-sided confidence interval via finding the shortest length from this class is also considered. Necessary tables and computer program to actually apply these procedures are provided.

ISSN:0361-0918    

DOI:10.1080/03610917808812071

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

The parameters γ and δ of the Johnson Sudistribution are obtained from a zero of a 24-th order polynomial with coefficients depending on the reduced moment coefficients β1and β2.

ISSN:0361-0918    

DOI:10.1080/03610917808812072

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

In this paper a finite series approximation involving Laguerre polynomials is derived for central and noncentral multivariate gamma distributions. It is shown that if one approximates the density of any k nonnegative continuous random variables by a finite series of Laguerre polynomials up to the (n1, …, nk)th degree, then all the mixed moments up to the order (n1, …, nk) of the approximated distribution equal to the mixed moments up to the same order of the random variables. Some numerical results are given for the bivariate central and noncentral multivariate gamma distributions to indicate the usefulness of the approximations.

ISSN:0361-0918    

DOI:10.1080/03610917808812073

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Numerical stability is but one of many desirable properties which should be considered when designing statistical software. However, rigorous roundoff analysis is rarely done because it seems not worth the price; the influence of rounding error is usually of secondary importance, and the analysis is thought to be beyond the reach of all but a few specialists. This note discusses the role of roundoff analysis in the design of a statistical program and shows that new techniques sometimes make assessment of the effect of rounding errors no more difficult than the verification of other program properties.

ISSN:0361-0918    

DOI:10.1080/03610917808812074

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Let x1, x2, … be a sequence of independent random vectorsfrom the p-variate von Mises-Fisher distribution with zero meandirection and concentration parameter K, and let Rmresultant length of x1, …, xm. In the decomposition, the two components are approximately independently distributed as x2-variates with respectivedegrees of freedom (p−1)(n−t−1) and (p−l)t, provided that k is of moderate size and that t is moderately small relative to n. Hence,is approximately distributed as an F-variate with degrees of freedom (p−l)t and (p−1)(n−t−1). Simulation studies for the cases p=2 and p=3, with t=l, suggest that this last approximation may be reasonable for k as low as 2.5, and n=5,6,… . Some recommendations for larger values of t are made, and an application to the theory of outliers for samples from von Mises-Fisher distributions is mentioned.

ISSN:0361-0918    

DOI:10.1080/03610917808812075

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

Exact tables for Spearman’s rho are available only for n ≤ 16 and no ties in the data. Some accurate methods of approximating the distribution with no ties present have been used to obtain approximate tables for larger values of n. Often ties are present in the data so these tables are no longer exact. Also sometimes the tables are not conveniently available to the user. In such situations an approximation that is both simple and accurate would be useful.

ISSN:0361-0918    

DOI:10.1080/03610917808812076

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

This paper demonstrates how certain statistics, computed from a sample of size n (from almost any distribution) may be simulated by using a sequence of substantially less than n random normal variates. Many statistics, θ, including almost all maximum likelihood estimates, can be expressed in terms of the sample trigonometric moments, STM. The STM are asymptotically multivariate normal with a mean vector and variance-covariance matrix easily expressible in terms of equally spaced characteristic function evaluations. Thus one only needs to know the Fourier transform or equivalently the characteristic function associated with elements of any moderate to large i. i. d. sample and have access to anormalrandom number generator to generate a sequence of STM with distributional properties almost identical to those of STM computed from that sample. These STM can in turn be used to compute the desired statistic θ.

ISSN:0361-0918    

DOI:10.1080/03610917808812077

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610917808812070

出版商:Marcel Dekker, Inc    

年代:1978

数据来源: Taylor