摘要:

Conditional tests on the scale parameter of the gamma distribution with an unknown nuisance shape parameter are considered. Such tests, based upon the conditional distribution of the sample mean x (or equivalentlyWi, = x/x) given the geometric mean x, are uniformly most powerful unbiased tests. Percentage points of the conditional distribution are tabulated for small sample sizes and an asymptotic normal approximation is also obtained.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489502

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

J. F. Lawless [6] and G. S. Lingappaiah [8] constructed prediction intervals for future failure times based on times of early failures when life is exponentially distributed. Some aspects of these interesting papers are discussed here. Of special interest is the amount of information for prediction contained in the latest available failure time, relative to the amount of information in all of the failure times up to the latest one. It is found that this relative information is very high in small samples as well as asymptotically, regardless of the time of prediction or the time to be predicted. Recurrence relations for certain distribution functions which arise in connection with the prediction intervals are given and large sample properties of the prediction intervals of Lawless and Lingappaiah are derived. Conditions for the best linear unbiased predictor to be the best unbiased predictor are discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489503

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Tables of factors are given for complete samples of sizen(n= 20(1)40) for correcting small-sample bias in Hassanein's [4] asymptotically unbiased quantile estimators of extreme-value location and scale parameters. Hassanein'sk-order-statistic estimators of the two parameters are based on the same set of spacings for eachk(k= 2. … 10) and are asymptotically best of this type of linear estimator (with asymptotic efficiencies of .977 and .937, respectively, fork= 10). The tabulated values not only allow one to obtain estimates based on the specified set of ordered observations that are best linear unbiased or best linear invariant (for the specified set of weights), but they also enable one to use procedures described in Mann. Schafer, and Singpurwalla [13] to compute approximate confidence bounds and tolerance and prediction intervals. Also tabulated are efficiencies of unbiased versions of the estimators relative to Cramér-Rao bounds for regular unbiased estimators and to best linear unbiased estimators (where available). The efficiencies of the ten-order-statistic unbiased estimators relative to the best linear unbiased estimators (compared for samples of sizes 20 through 25) are very close to I.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489504

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A new expression is obtained for the minimum variance unbiased estimator ofP[Y<X] under the assumption thatXandYare independent normal random variables. This new expression yields approximations to the UMVUE which are superior to those previously used by Church and Harris [1] and Downton [2].

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489505

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A graphical trial-and-error approach has been outlined for the derivation of single-stage attribute acceptance-sampling plans in which either the Acceptable Quality Level or the Lot, Tolerance Fraction Defective is larger than 0.5. The solution procedure tlses Larson's nomograph of the cumulative binomial distribution. A numerical example is provided.

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489506

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489507

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489509

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489511

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489514

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1977.10489515

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor