摘要:

Some of the distributional properties of the moment estimator (ρ*) for the shape parameter, ρ, of the two parameter gamma distribution are determined and compared with previously known results for the maximum likelihood estimatorand Thom’s estimator (ρT). Methods are described for finding approximations to the percentage points and cumulative distribution function of ρ*. Two graphs are given which permit the computation of confidence Intervals for ρ based on ρ*computed from a sample of n observations. The first four sampling moments of p*, found by Monte Carlo simulation, are compared, are compared with previously known sampling moments forand ρT.

ISSN:0361-0918    

DOI:10.1080/03610917708812023

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

A numerical method for obtaining data (X|y), relative to the linear model, is given. The user is allowed to specify column means for the X matrix, the general order of condition number, the unique L1solution vectorand the deviations of y's about the fitted hyperplane. Implementation of the method requires little more than use of subroutines found in most modern subroutine libraries. Computer generated data of this kind are useful in numerical studies of the operating characteristics of different algorithms.

ISSN:0361-0918    

DOI:10.1080/03610917708812024

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

Friedman’s (1937, 1940) S-statistic is designed to test the hypothesis that there is no treatment effect in a randomized-block design with k treatments and n blocks. In this paper we give tables of the null distribution of S for k = 5, n = 6(1)8, and for k = 6, n = 2(1)6. Computational details are discussed.

ISSN:0361-0918    

DOI:10.1080/03610917708812025

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

In this paper we consider a rank test for trend. The data is given in the form of a two-way layout from k treatments and n blocks. For testing the hypothesis that there is no treatment effect, against the alternative that the treatment effects are, in a specified order, theL-test was proposed by Page (1963). In this paper a recurrence formula is derived for computing the exact distribution ofL. Tables of exact probabilities and critical values are given for nominal values of α = 0. 2, 0. 1, 0. 05, 0. 025, 0. 01, 0. 005, and 0. 001, fork= 3(1)8, n = 2(1)10.

ISSN:0361-0918    

DOI:10.1080/03610917708812026

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

In this paper subroutines are given which calculate the uniformly minimum variance unbiased estimators (UMVUE’ s) of a broad class of functions of the parameters of the normal and gamma distributions. These subroutines employ the new expressions for the UMVUE’ s given recently by Gray, Watkins, and Schucany (1973), Woodward and Gray (1975), and Gray, Schucany, and Woodward (1976). In order to employ the subroutines here the user need only be able to provide a FORTRAN function subprogram to calculate derivatives of the function, either analytically or numerically.

ISSN:0361-0918    

DOI:10.1080/03610917708812027

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

An approximation is given to calculate V, the covariance matrix for normal order statistics. The approximation gives considerable improvement over previous approximations, and the computing algorithm is available from the authors.

ISSN:0361-0918    

DOI:10.1080/03610917708812028

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

An upper bound for any linear function of normed residuals from a least squares analysis of a linear model is determined by considering the non negative definitive property of the variance-covariance matrix of the residuals from another linear model. The basic result has a particularly simple form and is appropriate for the general linear model. It is developed using generalized inverse matrices and is therefore applicable to residuals from analyses of models with design matrices of less than full rank. One area of application of the upper bound is in the determination of exact percentage points of test statistics used to detect outliers in experiments. This is illustrated by deriving an upper bound for the second largest absolute normed residual for a particular class of designs. This upper bound may be used to show that certain percentage points of the maximum normed residual are obtainable exactly from appropriate F-distributions.

ISSN:0361-0918    

DOI:10.1080/03610917708812029

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

For the invariant unbiased level-α test of equality of two co-variance matrices, the quantities b and B satisfying the equations P(b≤T≤B) = 1-α, E(T|b≤T≤B) = E(T), where T is the mean trace of a multivariate beta, are required. Five and one per cent values of B are tabulated for m = 2,3(2)11,16; b can be obtained from B. Upper five and one per cent values of T are also included, as these are required for the locally most powerful invariant test of nullity of any source of difference in several mean vectors and the locally most powerful invariant one-sided test of equality of two covariance matrices. Lower critical values may be obtained from upper critical values.

ISSN:0361-0918    

DOI:10.1080/03610917708812030

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

By appealing only to well-known results in linear programming, this note will prove that the normal equations are always consistent.

ISSN:0361-0918    

DOI:10.1080/03610917708812031

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610917708812022

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor