Small sample confidence intervals for the mean of a positively skewed distribution

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T1 , T3 and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T1, mad T1 , median T3 and the mad T3. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T1 and median T3 outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T3 outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

Population structure of spotted sunfish (Lepomis punctatus) in the Florida Everglades as revealed by DNA microsatellite analysis

Genetic diversity can be used to describe patterns of gene flow within and between local and regional populations. The Florida Everglades experiences seasonal fluctuations in water level that can influence local population extinction and recolonization dynamics. In addition, this expansive wetland has been divided into water management regions by canals and levees. These combined factors can affect genetic diversity and population structure of aquatic organisms in the Everglades. We analyzed allelic variation at six DNA microsatellite loci to examine the population structure of spotted sunfish (Lepomis punctatus) from the Everglades. We tested the hypothesis that recurrent local extinction and recent regional divisions have had an effect on patterns of genetic diversity. No marked differences were observed in comparisons of the heterozygosity values of sites within and among water management units. No evidence of isolation by distance was detected in a gene flow and distance correlation between subpopulations. Confidence intervals for the estimated F-statistic values crossed zero, indicating that there was no significant genetic difference between subpopulations within a region or between regions. Notably, the genetic variation among subpopulations in a water conservation area was greater than variation among regions (Fsp>FPT). These data indicate that the spatial scale of recolonization following local extinction appears to be most important within water management units.

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.

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

Effect of delay of first interview and repetition of interview on accuracy and confidence of recall of a flashbulb -type memory

Hearing of the news of the death of Diana, Princess of Wales, in a traffic accident, is taken as an analogue for being a percipient but uninvolved witness to a crime, or a witness to another person's sudden confession to some illegal act. This event (known in the literature as a “reception event”) has previously been hypothesized to cause one to form a special type of memory commonly known as a “flashbulb memory” (FB) (Brown and Kulik, 1977). FB's are hypothesized to be especially resilient against forgetting, highly detailed including peripheral details, clear, and inspiring great confidence in the individual for their accuracy. FB's are dependent for their formation upon surprise, emotional valence, and impact, or consequentiality to the witness of the initiating event. FB's are thought to be enhanced by frequent rehearsal. FB's are very important in the context of criminal investigation and litigation in that investigators and jurors usually place great store in witnesses, regardless of their actual accuracy, who claim to have a clear and complete recollection of an event, and who express this confidently. Therefore, the lives, or at least the freedom, of criminal defendants, and the fortunes of civil litigants hang on the testimony of witnesses professing to have FB's. ^ In this study, which includes a large and diverse sample (N = 305), participants were surveyed within 2–4 days after hearing of the fatal accident, and again at intervals of 2 and 4 weeks, 6, 12, and 18 months. Contrary to the FB hypothesis, I found that participants' FB's degraded over time beginning at least as early as two weeks post event. At about 12 months the memory trace stabilized, resisting further degradation. Repeated interviewing did not have any negative affect upon accuracy, contrary to concerns in the literature. Analysis by correlation and regression indicated no effect or predictive power for participant age, emotionality, confidence, or student status, as related to accuracy of recall; nor was participant confidence in accuracy predicted by emotional impact as hypothesized. Results also indicate that, contrary to the notions of investigators and jurors, witnesses become more inaccurate over time regardless of their confidence in their memories, even for highly emotional events. ^

A theoretical analysis of eyewitness identification: Dual -process theory, signal detection theory and eyewitness confidence

Given the growing number of wrongful convictions involving faulty eyewitness evidence and the strong reliance by jurors on eyewitness testimony, researchers have sought to develop safeguards to decrease erroneous identifications. While decades of eyewitness research have led to numerous recommendations for the collection of eyewitness evidence, less is known regarding the psychological processes that govern identification responses. The purpose of the current research was to expand the theoretical knowledge of eyewitness identification decisions by exploring two separate memory theories: signal detection theory and dual-process theory. This was accomplished by examining both system and estimator variables in the context of a novel lineup recognition paradigm. Both theories were also examined in conjunction with confidence to determine whether it might add significantly to the understanding of eyewitness memory. ^ In two separate experiments, both an encoding and a retrieval-based manipulation were chosen to examine the application of theory to eyewitness identification decisions. Dual-process estimates were measured through the use of remember-know judgments (Gardiner & Richardson-Klavehn, 2000). In Experiment 1, the effects of divided attention and lineup presentation format (simultaneous vs. sequential) were examined. In Experiment 2, perceptual distance and lineup response deadline were examined. Overall, the results indicated that discrimination and remember judgments (recollection) were generally affected by variations in encoding quality and response criterion and know judgments (familiarity) were generally affected by variations in retrieval options. Specifically, as encoding quality improved, discrimination ability and judgments of recollection increased; and as the retrieval task became more difficult there was a shift toward lenient choosing and more reliance on familiarity. ^ The application of signal detection theory and dual-process theory in the current experiments produced predictable results on both system and estimator variables. These theories were also compared to measures of general confidence, calibration, and diagnosticity. The application of the additional confidence measures in conjunction with signal detection theory and dual-process theory gave a more in-depth explanation than either theory alone. Therefore, the general conclusion is that eyewitness identifications can be understood in a more complete manor by applying theory and examining confidence. Future directions and policy implications are discussed. ^