摘要:

We obtain tight upper and lower bounds on the coefficient of variation of mixtures of m probability distributions on [0,∞). The lower bound is explicit; the upper bound is computed by an elementary algorithm. In some particular cases, the upper bound may also be obtained in an analytically explicit form.

ISSN:0361-0918    

DOI:10.1080/03610918208812286

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

The X2approximation to the distribution of the sample coefficient of variation of a normally distributed random variable, due to McKay 1932 is not nearly as accurate as suggested by the confirmatory studies of Fieller 1932 and Pearson 1932.The approximation will, however, be adequate in many practical situations and has the convenience of requiring nothing more than the readily available tables of x2.

ISSN:0361-0918    

DOI:10.1080/03610918208812287

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Small sample tables are not available for the multisample multivariate rank sum test (MMRST) or the multisample multivariate median test (MMMT) LNstatistic. Consequently, the statistic usually is compared to its asymptotic Chi-square value. To investigate the appropriateness of this procedure a Monte Carlo study is used to measure both significance level and relative power for a variety of multivariate dispersion structures.

ISSN:0361-0918    

DOI:10.1080/03610918208812288

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

This paper gives the results of a new simulation study for the familiar calibration problem and the less familiar inverse median estimation problem. The latter arises when one wishes to estimate from a linear regression analysis the value of the independent variable corresponding to a specified value of the median of the dependent variable. For example, from the results of a regression analysis between stress and time to failure, one might wish to estimate the stress at which the median time to failure is 10,000 hours. In the study, the mean square error, Pitman closeness, and probability of overestimation are compared for both the calibration problem and the inverse median estimation problem for (1) the classical estimator, (2) the inverse estimator, and (3) a modified version of an estimator proposed by Naszodi (1978) for both a small sample and a moderately large sample situation.

ISSN:0361-0918    

DOI:10.1080/03610918208812289

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Providing certain parameters are known, almost any linear map from RPto R1can be adjusted to yield a consistent and unbiased estimator in the context of estimating the mixing proportion θ on the basis of an unclassified sample of observations taken from a mixture of two p-dimensional distributions in proportions θ and 1-θ. Attention is focused on an estimator proposed recently, θ, which has minimum variance over all such linear maps. Unfortunately, the form of θ depends on the means of the component distributions and the covariance matrix of the mixture distribution. The effect of using appropriate sample estimates for these unknown parameters in forming θ is investigated by deriving the asymptotic mean and variance of the resulting estimator. The relative efficiency of this estimator under normality is derived. Also, a study is undertaken of the performance of a similar type of estimator appropriate in the context where an observed data vector is not an observation from either one or the other onent distributions, but is recorded as an integrated measurement over a surface area which is a mixture of two categories whose characteristics have different statistical distributions.The asymptotic bias in this case is compared with some available practical results.

ISSN:0361-0918    

DOI:10.1080/03610918208812290

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Sample size procedures of T- and F-tests for some nonnormal distributions are discussed. An adaptation to the Kruskal-Wallis and Friedman tests is mentioned.

ISSN:0361-0918    

DOI:10.1080/03610918208812291

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

A discrete distribution called the log-zero-Poisson distribution has been recommended by Katti (c.f. Biometrics 1970) as an alternate to the negative binomial and other distributions usually called "contagious" distributions.A major problem in the use of this and all other contagious distributions has been the difficulty of obtaining the maximum likelihood esti-mates. A custom-made ad hoc estimator, λ, has been proposed for the parameter λ of this distribution in Katti and Khedr (1980). In this paper, its efficiency relative to Fisher information is studied, only to discover that λ can be 30 times better than the maximum likelihood estimate in some parts of the parameter space and much weaker in other parts.A preliminary test is recommended to choose between the estimates, and the efficiency of the procedure is tabulated. As it is to be expected, the resultant estimator equals the better of the two estimators with some error at the values of the parameters where the two estimators are equivalent.

ISSN:0361-0918    

DOI:10.1080/03610918208812292

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

The problem of updating a discriminant function on the basis of data of unknown origin is studied. There are observations of known origin from each of the underlying populations, and subsequently there is available a limited number of unclassified observations assumed to have been drawn from a mixture of the underlying populations. A sample discriminant function can be formed initially from the classified data. The question of whether the subsequent updating of this discriminant function on the basis of the unclassified data produces a reduction in the error rate of sufficient magnitude to warrant the computational effort is considered by carrying out a series of Monte Carlo experiments. The simulation results are contrasted with available asymptotic results.

ISSN:0361-0918    

DOI:10.1080/03610918208812293

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

摘要:

Properties of proposed parametric and nonparametric tests for the problem of validating stochastic simulation models are discussed. Asymptotic efficiencies for various types of alternatives are developed for some of the tests. Numerical procedures along with simulation methods are used to evaluate the adequacy of normal approximations to the null distributions of the statistics and the small-sample power of the tests.

ISSN:0361-0918    

DOI:10.1080/03610918208812294

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610918208812285

出版商:Marcel Dekker, Inc.    

年代:1982

数据来源: Taylor