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The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include zeros, a simple confidence interval (CI) that is obtained by modifying Tian's [Inferences on the mean of zero-inflated lognormal data: the generalized variable approach. Stat Med. 2005;24:3223—3232] generalized CI, is proposed. A fiducial upper confidence limit (UCL) and a closed-form approximate UCL for an upper percentile are developed. Our simulation studies indicate that the proposed methods are very satisfactory in terms of coverage probability and precision, and better than existing methods for maintaining balanced tail error rates. The proposed CI and the UCL are simple and easy to calculate. All the methods considered are illustrated using samples of data involving airborne chlorine concentrations and data on diagnostic test costs. [ABSTRACT FROM AUTHOR]

Interval estimation procedures for the ratio of two Poisson means, weighted average of Poisson rates, and product of powers of Poisson means are considered. We propose a confidence interval (CI) based on the modified large sample (MLS) approach, and compare with the Cox CIs and the Wilson-score CIs. Our numerical studies indicate that the MLS CI is comparable with the Cox CI, and offers improvement in some cases. We also provide MLS CI for a weighted sum of Poisson means and compare with the available approximate CIs. The methods are illustrated using two examples. [ABSTRACT FROM PUBLISHER]

The problem of testing the equality of coefficients of variation of independent normal populations is considered. For comparing two coefficients, we consider the signed-likelihood ratio test (SLRT) and propose a modified version of the SLRT, and a generalized test. Monte Carlo studies on the type I error rates of the tests indicate that the modified SLRT and the generalized test work satisfactorily even for very small samples, and they are comparable in terms of power. Generalized confidence intervals for the ratio of (or difference between) two coefficients of variation are also developed. A modified LRT for testing the equality of several coefficients of variation is also proposed and compared with an asymptotic test and a simulation-based small sample test. The proposed modified LRTs seem to be very satisfactory even for samples of size three. The methods are illustrated using two examples. [ABSTRACT FROM AUTHOR]

Abstract: Inferential procedures for estimating and comparing normal correlation coefficients based on incomplete samples with a monotone missing pattern are considered. The procedures are based on the generalized variable (GV) approach. It is shown that the GV methods based on complete or incomplete samples are exact for estimating or testing a simple correlation coefficient. Procedures based on incomplete samples for comparing two overlapping dependent correlation coefficients are also proposed. For both problems, Monte Carlo simulation studies indicate that the inference based on incomplete samples and those based on samples after listwise or pairwise deletion are similar, and the loss of efficiency by ignoring additional data is not appreciable. The proposed GV approach is simple, and it can be readily extended to other problems such as the one of estimating two non-overlapping dependent correlations. The results are illustrated using two examples. [Copyright &y& Elsevier]

The problems of constructing tolerance intervals (TIs) in random effects model and in a mixed linear model are considered. The methods based on the generalized variable (GV) approach and the one based on the modified large sample (MLS) procedure are evaluated with respect to coverage probabilities and expected width in various setups using Monte Carlo simulation. Our comparison studies indicate that the TIs based on the MLS procedure are comparable to or better than those based on the GV approach. As the MLS TIs are in closed-form, they are easier to compute than those based on the GV approach. TIs for a two-way nested model are also derived using the MLS method, and their merits are evaluated using simulation. The procedures are illustrated using a practical example. [ABSTRACT FROM PUBLISHER]

Abstract: Exact methods for constructing two-sided tolerance intervals (TIs) and tolerance intervals that control percentages in both tails for a location-scale family of distributions are proposed. The proposed methods are illustrated by constructing TIs for a normal, logistic, and Laplace (double exponential) distributions based on type II singly censored samples. Factors for constructing one-sided and two-sided TIs for a logistic distribution are tabulated for the case of uncensored samples. Factors for constructing TIs based on censored samples for all three distributions are also tabulated. The factors for all cases are estimated by Monte Carlo simulation. An adjustment to the tolerance factors based on type II censored samples is proposed so that they can be used to find approximate TIs based on type I censored samples. Coverage studies of the approximate TIs based on type I censored samples indicate that the approximation is satisfactory as long as the proportion of censored observations is no more than 0.70. The methods are illustrated using some practical examples. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we consider the problems of constructing confidence interval for a Weibull mean and setting prediction limits for future samples. Specifically, we construct upper prediction limits that include at least of samples from a Weibull distribution at each of locations. The methods are based on the concept of generalized variable approach. The procedures can be easily extended to the type II censored samples, and they can be used to find approximate inferential procedures for type I censored samples. The proposed methods are conceptually simple and easy to use. The results are illustrated using some practical examples. [Copyright &y& Elsevier]

The problem of comparing several alternate sampling devices to the Occupational Safety and Health Administration (OSHA) standard, or the comparison of several sampling devices among themselves, is considered. A test based on the OSHA criterion that states that "90% of the readings of the sampling device should be within ± 25% of the readings obtained by the standard" is developed. Type I error rates and powers of the test are studied using Monte Carlo simulation. The study indicates that the proposed test is quite satisfactory for applications. The method is illustrated using a simulated data set. [ABSTRACT FROM AUTHOR]

In this article, we point out some interesting relations between the exact test and the score test for a binomial proportion p. Based on the properties of the tests, we propose some approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power. Sample sizes required for the tests are tabulated for various values of p to attain a power of 0.80 at level 0.05. We also propose approximate and exact methods of computing sample sizes needed to construct confidence intervals with a given precision. Using the proposed exact methods, sample sizes required to construct 95% confidence intervals with various precisions are tabulated for p = .05(.05).5. The approximate methods for computing sample sizes for score confidence intervals are very satisfactory and the results coincide with those of the exact methods for many cases. [ABSTRACT FROM AUTHOR]

Abstract: This article concerns inference on the correlation coefficients of a multivariate normal distribution. Inferential procedures based on the concepts of generalized variables (GVs) and generalized -values are proposed for elements of a correlation matrix. For the simple correlation coefficient, the merits of the generalized confidence limits and other approximate methods are evaluated using a numerical study. The study indicates that the proposed generalized confidence limits are uniformly most accurate even for samples as small as three. The results are extended for comparing two independent correlations, overlapping and non-overlapping dependent correlations. For each problem, the properties of the GV approach and other asymptotic methods are evaluated using Monte Carlo simulation. The GV approach produces satisfactory results for all the problems considered. The methods are illustrated using a few practical examples. [Copyright &y& Elsevier]

The conventional approach for testing the equality of two normal mean vectors is to test first the equality of covariance matrices, and if the equality assumption is tenable, then use the two-sample Hotelling T2 test. Otherwise one can use one of the approximate tests for the multivariate Behrens–Fisher problem. In this article, we study the properties of the Hotelling T2 test, the conventional approach, and one of the best approximate invariant tests (Krishnamoorthy & Yu, 2004) for the Behrens–Fisher problem. Our simulation studies indicated that the conventional approach often leads to inflated Type I error rates. The approximate test not only controls Type I error rates very satisfactorily when covariance matrices were arbitrary but was also comparable with the T2 test when covariance matrices were equal. [ABSTRACT FROM AUTHOR]

Lot quality assurance sampling (LQAS) with two-stage sampling plan was applied for rapid monitoring of coverage after every round of mass drug administration (MDA). A Primary Health Centre (PHC) consisting of 29 villages in Thiruvannamalai district, Tamil Nadu was selected as the study area. Two threshold levels of coverage were used: threshold A (maximum: 60%; minimum: 40%) and threshold B (maximum: 80%; minimum: 60%). Based on these thresholds, one sampling plan each for A and B was derived with the necessary sample size and the number of allowable defectives (i.e. defectives mean those who have not received the drug). Using data generated through simple random sampling (SRSI) of 1750 individuals in the study area, LQAS was validated with the above two sampling plans for its diagnostic and field applicability. Simultaneously, a household survey (SRSH) was conducted for validation and cost-effectiveness analysis. Based on SRSH survey, the estimated coverage was 93.5% (CI: 91.7–95.3%). LQAS with threshold A revealed that by sampling a maximum of 14 individuals and by allowing four defectives, the coverage was ≥60% in >90% of villages at the first stage. Similarly, with threshold B by sampling a maximum of nine individuals and by allowing four defectives, the coverage was ≥80% in >90% of villages at the first stage. These analyses suggest that the sampling plan (14,4,52,25) of threshold A may be adopted in MDA to assess if a minimum coverage of 60% has been achieved. However, to achieve the goal of elimination, the sampling plan (9, 4, 42, 29) of threshold B can identify villages in which the coverage is <80% so that remedial measures can be taken. Cost-effectiveness analysis showed that both options of LQAS are more cost-effective than SRSH to detect a village with a given level of coverage. The cost per village was US $76.18 under SRSH. The cost of LQAS was US $65.81 and 55.63 per village for thresholds A and B respectively. The total financial cost of classifying a village correctly with the given threshold level of LQAS could be reduced by 14% and 26% of the cost of conventional SRSH method. [ABSTRACT FROM AUTHOR]

The inferential procedures based on an optimal combination of correlated estimators of the common mean of a multivariate normal distribution are considered. Exact properties of the conditional and unconditional confidence intervals due to Halperin [Halperin, 1961, Almost linearly-optimum combination of unbiased estimates. Journal of the American Statistical Association, 56, 36–43] are numerically evaluated. Our numerical studies show that the conditional confidence interval is slightly shorter than the unconditional confidence interval. A condition under which the conditional approach is advantageous over the best of the t procedures based on individual components is discussed. The methods are illustrated using an example. [ABSTRACT FROM AUTHOR]