Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.

Improved estimation of postmortem interval with Cardiac Troponin T and improved analytical methods

Accurate knowledge of the time since death, or postmortem interval (PMI), has enormous legal, criminological, and psychological impact. In this study, an investigation was made to determine whether the relationship between the degradation of the human cardiac structure protein Cardiac Troponin T and PMI could be used as an indicator of time since death, thus providing a rapid, high resolution, sensitive, and automated methodology for the determination of PMI. ^ The use of Cardiac Troponin T (cTnT), a protein found in heart tissue, as a selective marker for cardiac muscle damage has shown great promise in the determination of PMI. An optimized conventional immunoassay method was developed to quantify intact and fragmented cTnT. A small sample of cardiac tissue, which is less affected than other tissues by external factors, was taken, homogenized, extracted with magnetic microparticles, separated by SDS-PAGE, and visualized with Western blot by probing with monoclonal antibody against cTnT. This step was followed by labeling and available scanners. This conventional immunoassay provides a proper detection and quantitation of cTnT protein in cardiac tissue as a complex matrix; however, this method does not provide the analyst with immediate results. Therefore, a competitive separation method using capillary electrophoresis with laser-induced fluorescence (CE-LIF) was developed to study the interaction between human cTnT protein and monoclonal anti-TroponinT antibody. ^ Analysis of the results revealed a linear relationship between the percent of degraded cTnT and the log of the PMI, indicating that intact cTnT could be detected in human heart tissue up to 10 days postmortem at room temperature and beyond two weeks at 4C. The data presented demonstrates that this technique can provide an extended time range during which PMI can be more accurately estimated as compared to currently used methods. The data demonstrates that this technique represents a major advance in time of death determination through a fast and reliable, semi-quantitative measurement of a biochemical marker from an organ protected from outside factors. ^

Bayesian Estimation of Small Proportions Using Binomial Group Test

Group testing has long been considered as a safe and sensible relative to one-at-a-time testing in applications where the prevalence rate p is small. In this thesis, we applied Bayes approach to estimate p using Beta-type prior distribution. First, we showed two Bayes estimators of p from prior on p derived from two different loss functions. Second, we presented two more Bayes estimators of p from prior on π according to two loss functions. We also displayed credible and HPD interval for p. In addition, we did intensive numerical studies. All results showed that the Bayes estimator was preferred over the usual maximum likelihood estimator (MLE) for small p. We also presented the optimal β for different p, m, and k.