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The problems of constructing confidence intervals (CIs) for the proportions and functions of proportions in finite populations are considered. For estimating the proportion in a finite population, we propose a CI based on the generalized fiducial method and compare it with an exact CI and score CI. For the two-sample problems, we consider interval estimating the difference between two proportions, the ratio of two proportions and the ratio of odds. Our solutions for the two-sample problems are based on the fiducial approach and the method of variance estimate recovery. All the CIs are evaluated on the basis of their exact coverage probabilities and expected widths. The methods are illustrated using some practical examples. [ABSTRACT FROM AUTHOR]

Statistical methods for constructing confidence intervals for the probability content in a specified interval are proposed. Exact and approximate solutions based on the fiducial approach are described when the measurements on the variable of interest can be modelled by a location-scale (or log-location-scale) distribution. Methods are described for the normal, Weibull, two-parameter exponential and two-parameter Rayleigh distributions. For each case, the solutions are evaluated for their merits. Three examples, where it is desired to estimate the percentages of engineering products meet the specification limits, are provided to illustrate the methods. [ABSTRACT FROM AUTHOR]

The problems of computing two-sided tolerance intervals (TIs) and equal-tailed TIs for a location-scale family of distributions are considered. The TIs are constructed using one-sided tolerance limits with the Bonferroni adjustments and then adjusting the confidence levels so that the coverage probabilities of the TIs are equal to the specified nominal confidence level. The methods are simple, exact and can be used to find TIs for all location-scale families of distributions including log-location-scale families. The computational methods are illustrated for the normal, Weibull, two-parameter Rayleigh and two-parameter exponential distributions. The computational method is applicable to find TIs based on a type II censored sample. Factors for computing two-sided TIs and equal-tailed TIs are tabulated and R functions to find tolerance factors are provided in a supplementary file. The methods are illustrated using a few practical examples. [ABSTRACT FROM AUTHOR]

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]

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples. [ABSTRACT FROM AUTHOR]

Approximate closed-form confidence intervals (CIs) for estimating the difference, relative risk, odds ratio, and linear combination of proportions are proposed. These CIs are developed using the fiducial approach and the modified normal-based approximation to the percentiles of a linear combination of independent random variables. These confidence intervals are easy to calculate as the computation requires only the percentiles of beta distributions. The proposed confidence intervals are compared with the popular score confidence intervals with respect to coverage probabilities and expected widths. Comparison studies indicate that the proposed confidence intervals are comparable with the corresponding score confidence intervals, and better in some cases, for all the problems considered. The methods are illustrated using several examples. [ABSTRACT FROM AUTHOR]

A gambler in possession of R chips/coins is allowed N (> R ) pulls/trials at a slot machine. Upon pulling the arm, the slot machine realizes a random state i ɛ{1, ..., M } with probability p ( i ) and the corresponding positive monetary reward g ( i ) is presented to the gambler. The gambler can accept the reward by inserting a coin in the machine. However, the dilemma facing the gambler is whether to spend the coin or keep it in reserve hoping to pick up a greater reward in the future. We assume that the gambler has full knowledge of the reward distribution function. We are interested in the optimal gambling strategy that results in the maximal cumulative reward. The problem is naturally posed as a Stochastic Dynamic Program whose solution yields the optimal policy and expected cumulative reward. We show that the optimal strategy is a threshold policy, wherein a coin is spent if and only if the number of coins r exceeds a state and stage/trial dependent threshold value. We illustrate the utility of the result on a military operational scenario. [ABSTRACT FROM AUTHOR]

A modified normal-based approximation for calculating the percentiles of a linear combination of independent random variables is proposed. This approximation is applicable in situations where expectations and percentiles of the individual random variables can be readily obtained. The merits of the approximation are evaluated for the chi-square and beta distributions using Monte Carlo simulation. An approximation to the percentiles of the ratio of two independent random variables is also given. Solutions based on the approximations are given for some classical problems such as interval estimation of the normal coefficient of variation, survival probability, the difference between or the ratio of two binomial proportions, and for some other problems. Furthermore, approximation to the percentiles of a doubly noncentralFdistribution is also given. For all the problems considered, the approximation provides simple satisfactory solutions. Two examples are given to show applications of the approximation. [ABSTRACT FROM AUTHOR]

The problem of estimating the difference between two binomial proportions is considered. Closed-form approximate confidence intervals (CIs) and a fiducial CI for the difference between proportions are proposed. The approximate CIs are simple to compute, and they perform better than the classical Wald CI in terms of coverage probabilities and precision. Numerical studies indicate that these approximate CIs can be used safely for practical applications under a simple condition. The fiducial CI is more accurate than the approximate CIs in terms of coverage probabilities. The fiducial CIs, the Newcombe CIs, and the Miettinen–Nurminen CIs are comparable in terms of coverage probabilities and precision. The interval estimation procedures are illustrated using two examples. [ABSTRACT FROM AUTHOR]

The problem of comparing the means of two lognormal distributions based on samples with multiple detection limits is considered. Tests and confidence intervals for the ratio of the two means, based on pivotal quantities involving the maximum likelihood estimators, are proposed. The merits of the proposed approaches are evaluated by Monte Carlo simulation. Simulation study indicates that the procedures are satisfactory in terms of coverage probabilities of confidence intervals, and powers of tests. The proposed approach can also be applied to find confidence intervals for the difference between the means of the two lognormal distributions. Illustrative examples with a real data set and with a simulated data set are given. [ABSTRACT FROM AUTHOR]

India is a signatory to World Health Assembly resolution for elimination of lymphatic filariasis (LF) and National Health Policy has set the goal of LF elimination by 2015. Annual mass drug administration (MDA) is ongoing in endemic districts since 1996–97. Compliance rate is a crucial factor in achieving elimination and was assessed in three districts of Tamil Nadu for 10th and 11th treatment rounds (TRs). An in-depth study assessed the impact of social mobilization by drug distributors (DDs) in two areas from each of the three districts. Overall coverage and compliance for assessed TRs were 76.3 and 67.7% which is below the optimum level to achieve LF elimination. Modifiable determinants continue to be the reason for non-consumption even in the 11th TR and 20.8% were systematic non-compliers. In 76.4% of the cases, DDs failed to adhere to three mandatory visits as per the guidelines. Number of visits by DDs in relation to low and high MDA coverage areas showed a significant relationship (P ≤ 0.000). MDA is limited to drug distribution alone and efforts by DDs in preparing the community were inadequate. Probable means to meet the challenges in preparation of the community is discussed. [ABSTRACT FROM PUBLISHER]

Globally mosquito-borne lymphatic filariasis (LF) is targeted for elimination by 2020. Towards this goal, the scope of community-based vector control as a supplementary strategy to mass drug administration (MDA) was assessed through an intensive education campaign and evaluated using pre- and post-educational surveys in an intervention and comparison village in Tamil Nadu, South India. Environmental and entomological indicators for breeding sites and mosquito density were examined before and after the intervention. Significant (P < 0.05) increase in knowledge was observed in intervention area with regard to transmission and control of LF. Relative change between intervention and comparison villages before and after intervention was also significant (z = >1.96). Multiple mosquito control and personal protection methods were in use during the post-intervention assessment and was evident from the significantly (P < 0.05) higher average score. Breeding sources declined significantly (P < 0.05) in the intervention village with a significant relative change (z = 4.32). Significant reduction in per man-hour indoor resting density of mosquitoes was observed in the intervention area compared to baseline. The per capita cost for reducing 87% of the mosquito density was $ 0.32 indicating the effectiveness of community-based approach. The usefulness of this strategy in the elimination of LF is discussed. [ABSTRACT FROM PUBLISHER]

Abstract: The problems of constructing prediction intervals for the binomial and Poisson distributions are considered. Available approximate, exact and conditional methods for both distributions are reviewed and compared. Simple approximate prediction intervals based on the joint distribution of the past samples and the future sample are proposed. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are comparable to or better than the available ones in most cases. The methods are illustrated using two practical examples. [ABSTRACT FROM AUTHOR]

Abstract: The problem of interval estimation of the stress–strength reliability involving two independent Weibull distributions is considered. An interval estimation procedure based on the generalized variable (GV) approach is given when the shape parameters are unknown and arbitrary. The coverage probabilities of the GV approach are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is very satisfactory even for small samples. For the case of equal shape parameter, it is shown that the generalized confidence limits are exact. Some available asymptotic methods for the case of equal shape parameter are described and their coverage probabilities are evaluated using Monte Carlo simulation. Simulation studies indicate that no asymptotic approach based on the likelihood method is satisfactory even for large samples. Applicability of the GV approach for censored samples is also discussed. The results are illustrated using an example. [Copyright &y& Elsevier]

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]

This article considers the problem of testing and interval estimation of the reliability parameter P(Y1 < g2), where Y1 and Y2 are independent normal random variables with unknown means and variances. A new approximate method is proposed, and is compared with two existing approximate methods and a generalized variable method. Simulation studies indicate that the sizes of the existing approximate tests exceed the nominal level considerably in some situations while the new method controls the sizes satisfactorily in all situations considered. The studies also indicated that the generalized variable test is too conservative for small samples. A confidence limit for the reliability parameter based on the new approximate test is also given. The results are extended to the case where Y1 and depend on some explanatory variables. The methods are illustrated using three examples, and some recommendations are made regarding what method should be used for practical applications. [ABSTRACT FROM AUTHOR]

We consider the problem of deriving one-sided tolerance intervals in the one-way random model with balanced as well as unbalanced data, under the usual normality assumptions. The problems investigated deal with the computation of such intervals for the observable random variable, as well as the unobservable random effect in the one-way random model. The tolerance limits are derived using the concept of a generalized confidence interval. Some approximations are derived for the tolerance limits, and their performance is investigated by simulation. The simulation results show that the proposed tolerance limits are quite satisfactory for practical use. [ABSTRACT FROM AUTHOR]

Cet article présente une procédure simple et claire qui permet, dans une certaine mesure, l'estimation et le test de la probabilité d'une réponse erronée. De plus, cette méthode permet également d'estimer la proportion de la population en utilisant deux fois la méthode de réponse randomisée de Warner (1965). [ABSTRACT FROM AUTHOR]