We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD.
Abstract. In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure ∆. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision of some estimators of these overlap measures. Confidence intervals for the measures are also constructed via bootstrap methods and Taylor series approximation.Mathematics Subject Classification. 62F10, 62F40.
In this article, we introduce a bivariate sign test for the one-sample bivariate location model using a bivariate ranked set sample (BVRSS). We show that the proposed test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the non centrality parameter are derived. The asymptotic distribution of the vector of sample median as an estimator of the locations of the bivariate model is introduced. Theoretical and numerical comparisons of the asymptotic efficiency of the BVRSS sign test with respect to the BVSRS sign test are also given.
Regression is used to estimate the population mean of the response variable, , in the two cases where the population mean of the concomitant (auxiliary) variable, , is known and where it is unknown. In the latter case, a double sampling method is used to estimate the population mean of the concomitant variable. We invesitagate the performance of the two methods using extreme ranked set sampling (ERSS), as discussed by Samawi et al. (1996). Theoretical and Monte Carlo evaluation results as well as an illustration using actual data are presented. The results show that if the underlying joint distribution of and is symmetric, then using ERSS to obtain regression estimates is more efficient than using ranked set sampling (RSS) or simple random sampling (SRS).
The benchmark dose (BMD) methodology is a statistical procedure, first proposed by Crump in 1984, to determine allowable daily intakes of chemicals. The BMD was proposed as an alternative to the no‐observed‐adverse‐effect‐level (NOAEL) approach. The procedure is now widely used in risk assessment to establish health standards and guidelines for exposure of toxins to humans or to the environment. In this article, we review the BMD procedure, give details on how to compute the BMD and BMDL for both quantal and continuous endpoints and survey some of the recent developments in benchmark dose estimation.
The benchmark dose (BMD) methodology is a statistical procedure, first proposed by Crump in 1984, to determine allowable daily intakes of chemicals. The BMD was proposed as an alternative to the no‐observed‐adverse‐effect‐level (NOAEL) approach. The procedure is now widely used in risk assessment to establish health standards and guidelines for exposure of toxins to humans or to the environment. In this article, we review the BMD procedure, give details on how to compute the BMD and BMDL for both quantal and continuous endpoints and survey some of the recent developments in benchmark dose estimation.
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