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.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

The effects of government disability benefits, accessibility laws and rehabilitation on employment choices by individuals with spinal cord injuries

Greater inclusion of individuals with disabilities into mainstream society is an important goal for society. One of the best ways to include individuals is to actively promote and encourage their participation in the labor force. Of all disabilities, it is feasible to assume that individual with spinal cord injuries can be among the most easily mainstreamed into the labor force. However, less that fifty percent of individuals with spinal cord injuries work. ^ This study focuses on how disability benefit programs, such as Social Security Disability Insurance, and Worker's Compensation, the Americans with Disabilities Act and rehabilitation programs affect employment decisions. The questions were modeled using utility theory with an augmented expenditure function and indifference theory. Statically, Probit, Logit, predicted probability, and linear regressions were used to analyze these questions. Statistical analysis was done on the probability of working, ever attempting to work after injury, and on the number of years after injury that work was first attempted and the number of hours worked per week. The data utilized were from the National Spinal Cord Injury Database and the Spinal Cord Injuries and Labor Database. The Spinal Cord Injuries and Labor Database was created specifically for this study by the author. Receiving disability benefits decreased the probability of working, of ever attempting to work, increased the number of years after injury before the first work attempt was made, and decreased the number of hours worked per week for those individuals working. These results were all statistically significant. The Americans with Disabilities Act decrease the number of years before an individual made a work attempt. The decrease is statistically significant. The amount of rehabilitation had a significant positive effect for male individuals with low paraplegia, and significant negative effect for individuals with high tetraplegia. For women, there were significant negative effects for high tetraplegia and high paraplegia. ^ This study finds that the financial disincentives of receiving benefits are the major determinants of whether an individual with a spinal cord injury returns to the labor force. Policies are recommended that would decrease the disincentive. ^

Medical Curriculum at Selected Colleges: Foundations and Integrated Presentation of Basic Medical Sciences Distribution over Pre-Clerkship Period

Overview and statistics on the medical curriculum at Arizona, Emory, FIU, Rochester, and Vermont.

Integrating Technology in a Statistics Course for a Special Program at Florida International University

A special undergraduate program for selected biology majors was recently inaugurated at Florida International University. The curriculum emphasizes science, mathematics, and statistics. A statistics course was implemented for this program integrating PowerPoint, statistical software (SPSS), and data from biological/biomedical studies. This didactic experience is discussed here.

Fibrations and contact structures

We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms.

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

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.

The effects of government disability benefits, accessibility laws and rehabilitation on employment choices by individuals with spinal cord injuries

Greater inclusion of individuals with disabilities into mainstream society is an important goal for society. One of the best ways to include individuals is to actively promote and encourage their participation in the labor force. Of all disabilities, it is feasible to assume that individual with spinal cord injuries can be among the most easily mainstreamed into the labor force. However, less that fifty percent of individuals with spinal cord injuries work. This study focuses on how disability benefit programs, such as Social Security Disability Insurance, and Worker's Compensation, the Americans with Disabilities Act and rehabilitation programs affect employment decisions. The questions were modeled using utility theory with an augmented expenditure function and indifference theory. Statically, Probit, Logit, predicted probability, and linear regressions were used to analyze these questions. Statistical analysis was done on the probability of working, ever attempting to work after injury, and on the number of years after injury that work was first attempted and the number of hours worked per week. The data utilized were from the National Spinal Cord Injury Database and the Spinal Cord Injuries and Labor Database. The Spinal Cord Injuries and Labor Database was created specifically for this study by the author. Receiving disability benefits decreased the probability of working, of ever attempting to work, increased the number of years after injury before the first work attempt was made, and decreased the number of hours worked per week for those individuals working. These results were all statistically significant. The Americans with Disabilities Act decrease the number of years before an individual made a work attempt. The decrease is statistically significant. The amount of rehabilitation had a significant positive effect for male individuals with low paraplegia, and significant negative effect for individuals with high tetraplegia. For women, there were significant negative effects for high tetraplegia and high paraplegia. This study finds that the financial disincentives of receiving benefits are the major determinants of whether an individual with a spinal cord injury returns to the labor force. Policies are recommended that would decrease the disincentive.