摘要:

In statistics, Fourier series have been used extensively in such areas as time series and stochastic processes. These series; however, to a large degree have been neglected with regard to their use in statistical distribution theory. This omission appears quite striking when one considers that, after the elementary functions, the trigonometric functions are the most important functions in applied mathematics. In this paper a procedure is developed for utilizing Fourier series to represent distribution functions of finite range random variables as Fourier series with coefficients easily expressible (using Chebyshev polynomials) In terms of the moments of the distribution. This method allows the evaluation of probabilities for a wide class of distributions. It is applied to the

ISSN:0361-0918    

DOI:10.1080/03610917708812040

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

Data are often collected in histogram form, especially in the context of computer simulation. While requiring less memory and computation than saving all observations, the grouping of observations in the histogram cells complicates statistical estimation of parameters of interest. In this paper the mean and variance of the cell midpoint estimator of the pthquantile are analyzed in terms of distribution, cell width, and sample size. Three idiosyncrasies of using cell midpoints to estimate quantiles are illustrated. The results tend to run counter to previously published results for grouped data.

ISSN:0361-0918    

DOI:10.1080/03610917708812041

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

This case study demonstrates statistical design and analysis techniques applicable to any Monte Carlo or simulation experiment, namely a 27−3experimental design, antithetic variates, sample size determination, analysis of variance, regression analysis, and simultaneous inference. The example is a Monte Carlo investigation of the robustness of Bechhofer and Blumenthal’s multiple ranking procedure (MRP). The investigation shows that their procedure works often, but not always. Factors that make it break down, are identified.

ISSN:0361-0918    

DOI:10.1080/03610917708812042

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

This note investigates the efficiency of using near-best or approximate L1estimators as starting values in L1linear programming procedures. In particular, it is shown that the total computer time can often be reduced if one first computes the least squares estimator, β, and then adjust y to y - Xβ in Barrodale and Roberts’ improved algorithm.

ISSN:0361-0918    

DOI:10.1080/03610917708812043

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seem appropriate to make a comparison among the estimators through some “closeness to the true value” criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pit-man-closeness efficiency gives the “odds” in favor of one of the estimators being closer to the true value than is the other in a given situation. Through the use of Pitman-closeness efficiency, this paper compares (a) the maximum likelihood estimator, (b) the minimum variance unbiased estimator, (c) the best invariant estimator, and (d) the median unbiased estimator within a class of estimators which includes (a), (b), and (c). Mean squared efficiency is also discussed.

ISSN:0361-0918    

DOI:10.1080/03610917708812044

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

摘要:

Tables are given of confidence limits on tail areas, γ, of the normal distribution, where γ = P{Y ≥ L}, and where L is a given number, and Y is normally distributed with unknown mean, μ, and unknown variance, σ2.

ISSN:0361-0918    

DOI:10.1080/03610917708812045

出版商:Marcel Dekker, Inc.    

年代:1977

数据来源: Taylor

ISSN:0361-0918    

DOI:10.1080/03610917708812039

出版商:Marcel Dekker, Inc    

年代:1977

数据来源: Taylor