Detecting the dubious digits: Benford's law in forensic accounting

Kuldeep Kumar and Sukanto Bhattacharya Introduce an unexpected quality in natural numbers that can help to detect faked data     

Effect of detection methods on risk estimates of exposure to biosolids-associated human enteric viruses

This study illustrates the effect of virus detection methods on estimates of risks of infection of biosolids-associated viruses for occupational workers and residential population during a hypothetical exposure of biosolids. Five gastroenteritis-associated human enteric viruses--enteroviruses (echovirus-12, enteroviruse types 68-71), adenoviruses, rotaviruses, and noroviruses genotype--I-were considered to represent human enteric viruses for risk estimation purposes. Ingested viral doses were calculated using literature-reported total infectious virus concentrations (based on BGM and A549 cell lines) and genome copies (GCs) in Michigan dewatered and class B biosolids. Cell-line-based infectivity parameters (i.e., ratio of total infectious virus concentration to GCs) were developed for different viruses in biosolids to use GCs for calculating ingested viral dose, addressing the issue of integration of molecular methods with biosolids-based virus risk assessment. Use of virus concentrations from molecular methods (with and without using cell-line-based infectivity parameter) resulted in higher risk estimates than culture methods, indicating the effect of the virus detection method on risk estimates. Further, use of virus concentrations from A549 cell lines resulted in higher risk estimates compared to those from BGM cell lines, suggesting the need for a proper choice of cell lines in determining infectious viral dose. The Monte Carlo uncertainty analyses of estimates for risk of infection due to enteroviruses showed that enteroviruses concentration was the most important parameter influencing risk estimates, indicating the need for reducing associated uncertainty. More work is required to develop cell-line-based infectivity parameters for different virus concentration levels and sample matrix types using a cut-off-based approach.     

Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample

In this paper, a generalization of inverted exponential distribution is considered as a lifetime model [A.M. Abouammoh and A.M. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Statist. Comput. Simul. 79(11) (2009), pp. 1301–1315]. Its reliability characteristics and important distributional properties are discussed. Maximum likelihood estimation of the two parameters involved along with reliability and failure rate functions are derived. The method of least square estimation of parameters is also studied here. In view of cost and time constraints, type II progressively right censored sampling scheme has been used. For illustration of the performance of the estimates, a Monte Carlo simulation study is carried out. Finally, a real data example is given to show the practical applications of the paper.     

Selecting the Best Exponential Population When the Scale Parameters are Bounded

Consider k (≥ 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.     

Robust R-Estimation of a Consensus Value from Multi-Center Studies

We consider multi-center experiments (for determining a consensus value) conducted in possibly heterogeneous set-ups leading to unbalanced heteroscedastic one-way random effects models. When normality of both the random components and their homoscedasticity are in doubt, standard statistical methods may not be valid. Two robust R-estimators (for the common location parameter), based on signed-rank statistics, are proposed and their properties studied. When large heteroscedasticity is present or the distribution of random effect is abnormal, the proposed estimators perform better than the classical weighted least squares and selected estimators. This feature is illustrated with an arsenic in oyster tissue problem, along with some other simulation studies.     

Discriminating Between the Log-Normal and Log-Logistic Distributions

Log-normal and log-logistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this article, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion are investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions are used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We perform some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose, two data sets are analyzed.     

Constructions of Residual Treatment Effects Designs for Comparing Test Treatments with a Control

This article deals with residual treatment effects designs for the purpose of comparing v test treatments with a control treatment when the number of periods is no larger than v + 1. Control balanced residual treatment effects designs, which are Schur-optimal, are considered. Some methods of their construction are given.     

On the performance of the nearest proportional to size sampling design

Assuming a super-population model the expected variance of the generalized difference estimator (Basu,1971) based on the nearest proportional to size sampling design introduced by Gabler(1987) is shown to be less than that of the same estimator based on an arbitrary sampling design from which the former design is realized. The former strategy is also shown to fare better than an unbiased ratio-cum-generalized difference estimator based on the nearest proportional to size sampling design in the sense of having less expected design variance under the same model.     

Estimating common standard deviation of two normal populations with ordered means

Independent random samples are taken from two normal populations with means $\mu _1$ and $\mu _2$ and a common unknown variance $\sigma ^2.$ It is known that $\mu _1\le \mu _2.$ In this paper, estimation of the common standard deviation $\sigma $ is considered with respect to a scale invariant loss function. A general minimaxity result is proved and a class of minimax estimators is derived. An admissibility result is proved in this class. Further a class of equivariant estimators with respect to a subgroup of affine group is considered and dominating estimators in this class are obtained. The risk performance of some of these estimators is compared numerically.     

Calibration Approach-based Product Estimator of Finite Population Total with Subsampling of Nonrespondents under Single and Two-phase Sampling

Hansen and Hurwitz (1946) technique–based estimator of population total is proposed using the calibration approach under the assumption that the auxiliary variable is negatively correlated with the study variable. The variance estimation is also considered. The two-phase sampling case is also explored. The theoretical results are demonstrated through empirical studies using both generated and real population data. The proposed estimator of population total outperforms the existing estimators in terms of the criteria of relative bias and relative root mean square error.