摘要:

In many engineering problems it is necessary to draw statistical inferences on the mean of a lognormal distribution based on a complete sample of observations. Statistical demonstration of mean time to repair (MTTR) is one example. Although optimum confidence intervals and hypothesis tests for the lognormal mean have been developed, they are difficult to use, requiring extensive tables and/or a computer. In this paper, simplified conservative methods for calculating confidence intervals or hypothesis tests for the lognormal mean are presented. In this paper, “conservative” refers to confidence intervals (hypothesis tests) whose infimum coverage probability (supremum probability of rejecting the null hypothesis taken over parameter values under the null hypothesis) equals the nominal level. The term “conservative” has obvious implications to confidence intervals (they are “wider” in some sense than their optimum or exact counterparts). Applying the term “conservative” to hypothesis tests should not be confusing if it is remembered that this implies that their equivalent confidence intervals are conservative. No implication of optimality is intended for these conservative procedures. It is emphasized that these are direct statistical inference methods for the lognormal mean, as opposed to the already well-known methods for the parameters of the underlying normal distribution. The method currently employed in MIL-STD-471A for statistical demonstration of MTTR is analyzed and compared to the new method in terms of asymptotic relative efficiency. The new methods are also compared to the optimum methods derived by Land (1971, 1973).

ISSN:0361-0918    

DOI:10.1080/03610918808812726

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

An expression for calculating the incomplete beta cumulative distributionIx(a, b) is given in terms of the seriesand its derivative whereFor small values of w, the expression is convenient for numerical calculation. For integer values of a, b, closed form expressions are also given.

ISSN:0361-0918    

DOI:10.1080/03610918808812727

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

The uniformly most powerful unbiased test in exponential family situations involving the F-distrlbution is illustrated with examples. Its performance is compared with that of the more conventional equal-tails test. A FORTRAN program for computing the critical values and tail sizes of this test is also presented.

ISSN:0361-0918    

DOI:10.1080/03610918808812728

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

The Institute of Mathematical Statistics has published a table of critical values for the multivariate extreme deviate test.However, the critical values, derived by a Monte Carlo simulation, are given for only the dimensions 2 through 5. We present new critical values for the dimensions 6 through 10, 12, 15, and 20. The results are presented in both table and graphical form. All critical values for the test statistic have been generated by a Monte Carlo simulation using 10,000 observations per case. An example is presented using the newcritical values.

ISSN:0361-0918    

DOI:10.1080/03610918808812729

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.

ISSN:0361-0918    

DOI:10.1080/03610918808812730

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.

ISSN:0361-0918    

DOI:10.1080/03610918808812731

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

A general testing procedure is proposed to multivariately test for equality of p variances among k groups. The procedure applies a multivariate analysis of variance on an appropriate measure of spread for the uncensored original observations. Three such measures of spread are compared in a simulation experiment which considered two and three variables with equal and unequal sample sizes for the null and alternative hypotheses for Gaussian, Student's t (8, 12, and 20 degrees of freedom) and gamma (α=2,4,6 and 10) distributions . The likelihood ratio test (Box, 1949) was included in the above simulations. The results suggest that if one chooses a measure of spread appropriate for the distribution of the original observations, the proposed MANOVA-based testing procedure is robust and reasonably powerful. Using this procedure for the normal distribution, similar power was observed to that of the likelihood ratio test when the variables were uncorrelated or had little positive correlation.

ISSN:0361-0918    

DOI:10.1080/03610918808812732

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

Several variance estimators using auxiliary information were compared for estimating the variance of the total or ratio under a one unit per stratum sample design. The auxiliary information used consisted of data from the 1977 and 1982 Economic Census. One thousand probability proportional to size one primary sampling unit per stratum samples were selected for the Monte Carlo study of characteristics of interest in a content evaluation survey as part of the 1982 Economic Census program. Six variance estimators were applied to each sample and their bias and mean square errors were evaluated. The results are strikingly different between the variance estimators of the estimated total and ratio.

ISSN:0361-0918    

DOI:10.1080/03610918808812733

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

The Edgeworth expansion for the distribution function of Spearman's rank correlation coefficient may be used to show that the rates of convergence for the normal and Pearson type II approximations are l/nand l/n2respectively. Using the Edgeworth expansion up to terms involving the sixth moment of the exact distribution allows an approximation with an error of order l/n3.

ISSN:0361-0918    

DOI:10.1080/03610918808812734

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor

摘要:

Sample kurtosis is a member of the large class of absolute moment tests of normality. We compare kurtosis to other absolute moment tests to determine which are the most powerful at detecting long‐tailed symmetric departures from normality for large samples. The large sample power of the tests is calculated using Geary's (1947) approximations of the moments of the test statistics. Using the system of Gram-Charlier symmetric distributions as alternatives, the most power is obtained using a moment in the range 2.5 ‐ 3.5.

ISSN:0361-0918    

DOI:10.1080/03610918808812735

出版商:Marcel Dekker, Inc.    

年代:1988

数据来源: Taylor