ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488788

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Monte Carlo estimates have been obtained for two quantities of interest in a discriminant analysis involving the usual linear discriminant function. The first is the unconditional probability of correct classification; the second is the expected value of its estimate based on the calculated Mahalanobis distance.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488789

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Considerkindependent normal populations with unknown means and a common unit variance and let a better population be defined to be one with a larger absolute value of the mean. The problem of selecting thetbest ofkpopulations is considered; the common number of observations from each population is determined so that the probability of a correct selection is not less than a specified quantity whenever the parameters lie in a pre-assigned parametric sub-space. A procedure for this problem is proposed and tables and bounds for probability of a correct selection are provided; some properties of the proposed procedure are also discussed. The problem of selecting a small non-empty subset containing the best population is also considered; a procedure is proposed and the constant involved in the procedure is determined so that the probability of a correct selection is not less than a specified quantity. The expected size of the selected subset is derived and its supremum obtained. Two secondary problems for determining the common sample size are discussed. The case when the common variance is unknown is also considered. The dual problem of selecting a subset containing the worst population is also treated.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488790

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

This paper treats multiple sequential sampling plans for attributes as finite Markov chains, and thereby demonstrates methods for evaluating various properties of such plans. Procedures for obtaining points on the operating characteristic curves and for computing the average total number of items sampled are provided.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488791

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this paper we discuss a probabilistic model of failure due to competing causes of failure operating on a unit during its lifetime. Following Cox we term this the Multi-Risk Model. We impose some well-known parametric forms on the underlying distributions of the model and obtain maximum likelihood estimates for the parameters of the distributions. The asymptotic variance-covariance matrix of the estimates is derived. We give examples using the exponential and Weibull distributions. The theory is applied to data published by Mendenhall and Hader, who studied a Single-Risk Model.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488792

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The inequality Pr (a≤Wi≤b;i= 1, 2, …,n) ≥ IInc=iPr (a≤Wi≤b) is shown to hold when the random variablesW1, …,Wn, have a particular multivariatef-distribution which is defined. It is used in this paper to construct conservative simultaneous prediction intervals for failure times in certain life test experiments. An additional inequality is shown to hold for all bivariate distributions belonging to a class of bivariatef-distributions which is defined. An indication of the use of this latter inequality is given. Some tables are included which indicate the sharpness of each of the inequalities.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488793

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Two methods are given for computing all possible regressions for a set of independent variables. One produces all the usual regression statistics; the other gives only the sums of squares of residuals. Both require less computation than other methods of computing all possible regressions and the second may compare favorably with the procedure suggested by Hocking and Leslie for finding the best subset without evaluating all possible subsets.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488794

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A class of nonparametric estimators off(x)based on a set ofnobservations has been proved by Parzen [l] to be consistent and asymptotically normal subject to certain conditions. Although quite useful for a wide variety of practical problems, these estimators have two serious disadvantages whennis large:1.Allnobservations must be stored in rapid-access storage.2.Evaluation off(x)for a particular value ofxrequires a long computation involving each of the observations.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488795

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The problem considered is that of minimizing a positive definite quadratic form subject to linear constraints. Mantel has conjectured that the constrained minimum must lie on that boundary which is farthest from the unconstrained minimum, where distance is measured by means of the given quadratic form. A counter-example is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488796

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Linear, asymptotically normal and efficient estimators are given for the shape parameter of the two parameter Weibull distribution when the scale parameter is known and for the log of the scale parameter when the shape parameter is known. The weights of the ordered observations and other constants needed for these estimators are readily obtainable from a previous article of the author.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488797

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor