摘要:

Suppose we wish to estimate the mean of some polynomial function of random variables from two independent Bernoulli populations, the parameters of which. rhemselves, are modeled as independent beta random variables. It. is assumed that the t.otal sample size for the experiment is fixed, but that the number of experimental units observed from each population may be random. This problem arises, ior example, when estimating the fault tolerance of a system by testing its compomentc individually. Using a decision theorebic approach, we seek to minimize the Bayes risk that arises from using a squared error loss function The Bayes estimator can lw detrmined in a straightforwardmanner, so the problem of optimal estimation rcduces. therefore, to a problem of optimallocatton of the samples between the two populatiorls. This can be solved via dynamic programming. Similar programming techniques are utilized to evaluate properties of a number of ad hoc allocation strategies that might also be collsidered for use in this problem.Two sample polynomials are analyzed along with a number of examples indicating the effects of different prior parameter settings. The effects of differences between prior pararueters used in the design and analysis stages of the experiment are also examined. For the polynomials considered, the adaptive strategies are found to be especially robust. We discuss computational techniques that facilitate such analyses by permitting rapid re-evaluation of strategies. Capabilities of this sort enrouragepeople to explorr designs more fully and to consider them from a number of different viewpuillts.

ISSN:0747-4946    

DOI:10.1080/07474949608836353

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

Bayesian sequentially planned tests of two simple hypotheses are discused. We provecontractivity of an iterated operator associated to Bellman's equation and justify thepolicy improvement method. finally we consider ε bayes tests and approximate thestopping bounds of the bayesian SPRT.

ISSN:0747-4946    

DOI:10.1080/07474949608836354

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

Let F be a strongly non-lattice distribution function with mean zero variance one, and a finite third moment.Let X1, X2,… be i.i.d. with common distribution function F. Let Sn= X1+ X2+…+ Xnand ξnbe random variables independent of Xn+1, Xn+2,…for n = 1,2,....The main results reported here are two limit theorems (Theorem 3 and Theorem 11) on occupation times for a type perturbed random walks Zn= Sn+ ξnwhen ξn's are slowly changing (also called slowly varying in this paper). A stone type local limit theorem, an Edgeworth expansion and an invariance principle are used in the proofs.

ISSN:0747-4946    

DOI:10.1080/07474949608836355

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

The paper proirides some sequential-type nonparanonparametric tests for tesiiriy ciie identity of two continuous bivariate distribution functions (d.f.'s) F1and F2when samples are drawn pairwise folllwing an inverse binomial scheme of sampling. various exacrt and large sample properties of the proposed tests are formulated and examined.

ISSN:0747-4946    

DOI:10.1080/07474949608836356

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

The steady state availability of 1-out-of-2 : G repairable system is obtained under the assumption that the life time of a component in standby position follows exponential distribution. It's nonparmetric estimator is proposed. The asymptotic properties of the estimator are used to provide the fixed width coinfience interval with specified coverage probability and testing of hypothesis problem using sequential procedure.

ISSN:0747-4946    

DOI:10.1080/07474949608836357

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

A control chart is proposed which applies a generalized sequential probability ratio test (SPRT) at fixed sampling intervals.the GSPRT chart, to monitor a parameter θ.which indexes a variable X with a genrnal distribution. Expression in terms of integral equations are developed for the moments of the zero-time and steady time to signal and number of observation to signal of the GSPRT chart. Comparsion are made between the performance of the GSPRT chart and the fixed sampling interval (FSI) and variable sampling interval (vsI) X and CUSUM charts. The GSPRT chart is found to be highly efficient and to have administrative advantages General Guidelines are provided for the design of GSPRT charts.

ISSN:0747-4946    

DOI:10.1080/07474949608836358

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We study a problem of scquentially comparing the number of species in two populations. We consider a sequential Bayesian approach which incorporates a sampling cost and a misclassification loss, and examine optimal and sub-optimal stopping rules. The optimal stopping rule is shown to be truncated when the prior distribution of the number of species is bounded. or when the prior is unbounded and satisfies certain conditions.

ISSN:0747-4946    

DOI:10.1080/07474946608836359

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949608836352

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor