The three-parameter lognormal distribution is widely used in many areas of science. Some modifications have been proposed to improve the maximum likelihood estimator. In some cases, however, the modified maximum likelihood estimates do not exist or the procedure encounters multiple estimates. The purpose of this research is focused on estimating the threshold or location parameter , because when is known, then the other two estimated parameters are obtained from the first two MLE equations. In this research, a method for constructing confidence intervals, confidence limits, and point estimator for the threshold parameter is proposed. Monte-Carlo simulation, bisection method, and SAS/IML were used to accomplish this objective. The bias of the point estimator and mean square error (MSE) criteria were used throughout extensive simulation to evaluate the performance of the proposed method. The result shows that the proposed method can provide quite accurate estimates.

Nutrient pollution has been identified as a significant threat to U.S. coastal and estuarine water quality. Though coastal and estuarine waters need nutrients to maintain a healthy, productive ecosystem, excess nutrients can lead to eutrophication. There are significant potential negative consequences associated with eutrophication, including loss of habitat, loss of economic activity, and direct threats to human health. Hillsborough Bay experienced eutrophication in the 1960s and 1970s due to a rapidly growing population and associated increases in nutrient pollution. These eutrophic conditions led to more frequent phytoplankton and macroalgae blooms and declines in seagrasses. To address these problems, a series of actions were taken including legislation limiting nutrient concentrations from domestic wastewater treatment plants, development of water quality and nutrient loading targets, and establishment of seagrass restoration and protection goals. Since the 1970s, water quality improvements and increasing seagrass acreages have been documented throughout Tampa Bay. In the current study, a series of analyses and tools are developed to obtain a more in depth understanding of water quality in Hillsborough Bay. The first tool is a linked hydrodynamic and water quality model (Environmental Fluid Dynamics Code) of Hillsborough Bay which can be employed to predict water quality responses to proposed management actions. In the second part of the study, a series of water quality indices were evaluated. The most appropriate index for determining overall water quality in Hillsborough Bay was identified. Chlorophyll a is one of the constituents in the water quality index and is currently used to evaluate annual water quality conditions in Hillsborough Bay. Therefore, the statistical distribution that describes chlorophyll a concentrations in Hillsborough Bay was identified and robust confidence intervals were developed to better understand the uncertainty associated with chlorophyll a measurements. Previous work linked chlorophyll a concentrations in Hillsborough Bay to explanatory variables based on monthly estimates. These relationships were used to develop water quality targets for the system. In this study, the previously developed relationship was revisited, resulting in an improved statistical model that is more robust. This improved model can also be used to evaluate the previously proposed targets and to better predict future changes due to climate change, sea level rise, and management actions. Lastly, a new method was developed to estimate atmospheric temperature in the contiguous United States.

Like coral reefs worldwide, the Florida Reef Tract has dramatically declined within the past two decades. Monitoring of 40 sites throughout the Florida Keys National Marine Sanctuary has undertaken a multiple-parameter approach to assess spatial and temporal changes in the status of the ecosystem. The objectives of the present study consist of the following: In chapter one, we review past coral reef studies; emphasis is placed on recent studies on the stony corals of reefs in the lower Florida Keys. We also review the economic impact of coral reefs on the state of Florida. In chapter two, we identify the underlying probability distribution function of the stony coral cover proportions and we obtain better estimates of the statistical properties of stony coral cover proportions. Furthermore, we improve present procedures in constructing confidence intervals of the true median and mean for the underlying probability distribution. In chapter three, we investigate the applicability of the normal probability distribution assumption made on the pseudovalues obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies. We investigate a new and more effective approach to estimating the Shannon-Wiener and Simpson's diversity index. In chapter four, we develop the best possible estimate of the probability distribution function of the jackknifing pseudovalues, obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies, using the xi nonparametric kernel density estimate method. This nonparametric procedure gives very effective estimates of the statistical measures for the jackknifing pseudovalues. Lastly, the present study develops a predictive statistical model for stony coral cover. In addition to identifying the attributable variables that influence the stony coral cover data of the lower Florida Keys, we investigate the possible interactions present. The final form of the developed statistical model gives good estimates of the stony coral cover given some information of the attributable variables. Our nonparametric and parametric approach to analyzing coral reef data provides a sound basis for developing efficient ecosystem models that estimate future trends in coral reef diversity. This will give the scientists and managers another tool to help monitor and maintain a healthy ecosystem.