摘要:

In this paper, we discuss the problem of estimating the mean and standard deviation of a logistic population based on multiply Type-II censored samples. First, we discuss the best linear unbiased estimation and the maximum likelihood estimation methods. Next, by appropriately approximating the likelihood equations we derive approximate maximum likelihood estimators for the two parameters and show that these estimators are quite useful as they do not need the construction of any special tables (as required for the best linear unbiased estimators) and are explicit estimators (unlike the maximum likelihood estimators which need to be determined by numerical methods). We show that these estimators are also quite efficient, and derive the asymptotic variances and covariance of the estimators. Finally, we present an example to illustrate the methods of estimation discussed in this paper.

ISSN:0233-1888    

DOI:10.1080/02331889508802516

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

A paradoxical behavior of thet-test underε-contamination is presented. The paradox consists in that under a fixed distribution of contaminants an increasing of the probability of the appearance of a contaminant may decrease the violation of the size of the test! A simple explanation of the phenomenon is given. It is revealed which contaminants make the test conservative and which make it liberal: it appears that, in spite of the established opinion, conservatism or liberalism of the test depends not so much on the tails of the contaminating distribution as on where its support is located.

ISSN:0233-1888    

DOI:10.1080/02331889508802517

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Considerk(≥ 2) independent exponential populations with different location and scale parameters. Call a population associated with largest of unknown location parameters as the best population. For the goal of selecting the best population, it is established that if the scale parameters are completely unknown, then the indifference-zone probability requirement can not be guaranteed by any single sample decision rule which is just and translation invariant. Under the assumption that the scale parameters are bounded above by a known constant, a single sample selection procedure is proposed for which the indifference-zone probability requirement can be guaranteed. Under the same assumption, 100P*% simultaneous upper confidence intervals for all distances from the largest location parameter are also obtained.

ISSN:0233-1888    

DOI:10.1080/02331889508802518

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

For the model considered by Chaturvedi, Pandey and Gupta (1991), two classes of sequential procedures are developed to construct confidence regions (which may be interval, ellipsoidal or spherical) of ‘pre-assigned width and coverage probability’ for the parameters of interest and for the minimum risk point estimation (taking loss to be quadratic plus linear cost of sampling) of the nuisance parameter. Second-Order approximations are derived for the expected sample size, coverage probability and ‘regret’ associated with the two classes of sequential procedures. A simple and direct method of obtaining the asymptotic distribution of the stopping time is provided. By means of examples, it is illustrated that several estimation problems can be tackled with the help of proposed classes of sequential procedures.

ISSN:0233-1888    

DOI:10.1080/02331889508802519

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Problems of estimation of a finite population total of a variable of sensitive in nature are studied under randomized response (RR) surveys. Some optimal sampling strategies are presented under different superpopulation models.

ISSN:0233-1888    

DOI:10.1080/02331889508802520

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Models for populations with immune or cured individuals but with others subject to failure are important in many areas, such as medical statistics and criminology. One method of analysis of data from such populations involves estimating an immune proportion 1 −pand the parameter(s) of a failure distribution for those individuals subject to failure. We use the exponential distribution with parameterλfor the latter and a mixture of this distribution with a mass 1 −pat infinity to model the complete data. This paper develops the asymptotic theory of a test for whether an immune proportion is indeed present in the population, i.e., forH0:p= 1. This involves testing at the boundary of the parameter space forp. We use a likelihood ratio test forH0. and prove that minus twice the logarithm of the likelihood ratio has as an asymptotic distribution, not the chi-square distribution, but a 50–50 mixture of a chi-square distribution with 1 degree of freedom, and a point mass at 0. The result is proved under an independent censoring assumption with very mild restrictions.

ISSN:0233-1888    

DOI:10.1080/02331889508802521

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:0233-1888    

DOI:10.1080/02331889208802505

出版商:Gordon & Breach Sceince Publishers    

年代:1995

数据来源: Taylor