New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

The Application of Fluorescent Nanocrystals to Study the Distribution of Neuropeptides in the Aedes Aegypti Mosquito

Semiconductor nanocrystals, also known as quantum dots (QDs), have been used in studies involving mice and human tissues, but never before in research on insects. We used QDs to study the distribution of two neuropeptides in the Aedes aegypti mosquito, the vector of both dengue and yellow fever. These neuropeptides play a significant role in the production of juvenile hormone, a hormone that controls biting behavior, metamorphosis, and reproduction throughout the life of the mosquito. The two neuropeptides allatostatin-C (AS-C) and allatotropin (AT) function as inhibitory (AS-C) and stimulatory (AT) regulators of juvenile hormone synthesis in the corpus allatum gland. In other insects, they also affect heart rate, gut movement, and nutrient uptake. Conjugating these neuropeptides to quantum dots via a streptavidinlbiotin link, we were able to expose the mosquito corpus allatum and abdomen to allatostatin-C and allatotropin and then to visualize their distribution under UV light using confocal and compound light microscopy. Histological sections of the whole mosquito, incubations of tissues with conjugates (in vitro), and microinjections of conjugates into the mosquito (in vivo) were performed. The results showed that quantum dots can be used to detect neuropeptide distribution in the mosquito. The more we understand about these neuropeptides and juvenile hormone, the more we can contribute to stopping the spread of infectious diseases, such as dengue and yellow fever.

Does the Pareto Distribution of Hurricane Damage Inherit its Fat Tail from a Zipf Distribution of Assets at Hazard?

Tropical Cyclones are a continuing threat to life and property. Willoughby (2012) found that a Pareto (power-law) cumulative distribution fitted to the most damaging 10% of US hurricane seasons fit their impacts well. Here, we find that damage follows a Pareto distribution because the assets at hazard follow a Zipf distribution, which can be thought of as a Pareto distribution with exponent 1. The Z-CAT model is an idealized hurricane catastrophe model that represents a coastline where populated places with Zipf- distributed assets are randomly scattered and damaged by virtual hurricanes with sizes and intensities generated through a Monte-Carlo process. Results produce realistic Pareto exponents. The ability of the Z-CAT model to simulate different climate scenarios allowed testing of sensitivities to Maximum Potential Intensity, landfall rates and building structure vulnerability. The Z-CAT model results demonstrate that a statistical significant difference in damage is found when only changes in the parameters create a doubling of damage.

Phylogenetic and ontogenetic influences on the distribution of anthocyanins and betacyanins in leaves of tropical plants

We examined the anatomy of expanding, mature, and senescing leaves of tropical plants for the presence of red pigments: anthocyanins and betacyanins. We studied 463 species in total, 370 genera, belonging to 94 families. This included 21 species from five families in the Caryophyllales, where betacyanins are the basis for red color. We also included 14 species of ferns and gymnosperms in seven families and 29 species with undersurface coloration at maturity. We analyzed 399 angiosperm species (74 families) for factors (especially developmental and evolutionary) influencing anthocyanin production during expansion and senescence. During expansion, 44.9% produced anthocyanins and only 13.5% during senescence. At both stages, relatively few patterns of tissue distributions developed, primarily in the mesophyll, and very few taxa produced anthocyanins in dermal and ground tissue simultaneously. Of the 35 species producing anthocyanins both in development and senescence, most had similar cellular distributions. Anthocyanin distributions were identical in different developing leaves of three heteroblastic taxa. Phylogeny has influenced the distribution of anthocyanins in the epidermis and mesophyll of expanding leaves and the palisade parenchyma during senescence, although these influences are not strong. Betacyanins appear to have similar distributions in leaves of taxa within the Caryophyllales and, perhaps, similar functions. The presence of anthocyanins in the mesophyll of so many species is inconsistent with the hypothesis of protection against UV damage or fungal pathogens, and the differing tissue distributions indicate that the pigments may function in different ways, as in photoprotection and freeradical scavenging.

Essays on investment, growth and income distribution

In this dissertation, I examine both theoretically and empirically the relationship between stock prices and income distribution using an endogenous growth model with social status impatience.^ The theoretical part looks into how status impatience and current economic status jointly determine time preference, savings, future economic status, stock prices, growth and wealth distribution in the steady state. This work builds on Burgstaller and Karayalcin (1996).^ More specifically, I look at (i) the effects of the distribution of status impatience levels on the distribution of steady state assets, incomes and consumption and (ii) the effects of changes in relative levels of status impatience on stock prices. Therefore, from (i) and (ii), I derive the correlation between stock prices, incomes and asset distribution. Also, the analysis of the stack market is undertaken in the presence of adjustment costs to investments.^ The empirical chapter looks at (i) the correlation between income inequality and long run economic growth on the one hand and (ii) the correlation between stock market prices and income inequality on the other. The role of stock prices and social status is examined to better understand the forces that enable a country to grow overtime and to determine why output per capita varies across countries. The data are from Summers and Heston (1988), Barro and Wolf (1989), Alesina and Rodrik (1994), Global financial Database (1997) and the World Bank. Data for social status are collected through a primary sample survey on the internet. Twenty-five developed and developing countries are included in the sample.^ The model developed in this study was specified as a system of simultaneous equations, in which per capita growth rate and income inequality were endogenous variables. Additionally, stock price index and social status measures were also incorporated. The results indicate that income inequality is inversely related to economic growth. In addition, increase in income inequality arising from higher stock prices constrains growth. Moreover, where social status is determined by income levels, it influences long run growth. Therefore, these results support findings of Persson and Tabellini (1994) and Alesina and Rodrik (1994). ^

Distribution and ecology of amphibians and reptiles in a fragmented landscape, northeastern Bolivia

Habitat loss and fragmentation have been implicated as driving forces behind recent waves of extinction. The regional landscape where this study occurred is a mosaic of forest and grassland, and therefore provides an ideal system with which to investigate the implications of habitat patchiness for the distribution and ecology of organisms. Here I describe patterns of amphibian and reptile distribution among and within habitats at the study site, investigate associations between habitat and community structure, describe nested subset patterns on forest islands, and quantify the relationship between body size and density across ecological scales and taxonomic groups. ^ Species richness did not vary across habitats, between forest island isolation classes or between island edges and cores. In contrast, species composition varied at all three ecological scales, reflecting differences in the distribution of both forest and open-habitat affiliated species. Species composition was associated with multivariate habitat profiles, with differences occurring along the isolation gradient of forest islands rather than the area gradient. The relationship between species composition and habitat was stronger for amphibians than for reptiles, a pattern that may be ascribed to physiological differences between the two groups. Analysis of nested subset pattern of community structure indicated that species composition of islands is nested as a function of isolation. Four species whose distribution on forest islands seems to be dispersal-limited drive the relationship between nestedness and isolation. Although there were several examples of shifts in body size across spatial scales and taxonomic groups, body size was not associated with density as predicted by theory, which may reflect differences between real and habitat islands, or differential responses of poikilothermic vertebrates to changes in density relative to homeotherms. ^ Taken together, the strongest result to emerge from this research is the importance of isolation, rather than area, on community structure in this system. Much evidence suggested that different ecological groups of species show distinct patterns of distribution both within and among habitat types. This suggests that species distributions at this site are not the result of 'neutral' processes at the community level, but rather reflect fundamental differences in the ecology of component species. ^

A methodology to estimate time varying user responses to travel time and travel time reliability in a road pricing environment

Road pricing has emerged as an effective means of managing road traffic demand while simultaneously raising additional revenues to transportation agencies. Research on the factors that govern travel decisions has shown that user preferences may be a function of the demographic characteristics of the individuals and the perceived trip attributes. However, it is not clear what are the actual trip attributes considered in the travel decision- making process, how these attributes are perceived by travelers, and how the set of trip attributes change as a function of the time of the day or from day to day. In this study, operational Intelligent Transportation Systems (ITS) archives are mined and the aggregated preferences for a priced system are extracted at a fine time aggregation level for an extended number of days. The resulting information is related to corresponding time-varying trip attributes such as travel time, travel time reliability, charged toll, and other parameters. The time-varying user preferences and trip attributes are linked together by means of a binary choice model (Logit) with a linear utility function on trip attributes. The trip attributes weights in the utility function are then dynamically estimated for each time of day by means of an adaptive, limited-memory discrete Kalman filter (ALMF). The relationship between traveler choices and travel time is assessed using different rules to capture the logic that best represents the traveler perception and the effect of the real-time information on the observed preferences. The impact of travel time reliability on traveler choices is investigated considering its multiple definitions. It can be concluded based on the results that using the ALMF algorithm allows a robust estimation of time-varying weights in the utility function at fine time aggregation levels. The high correlations among the trip attributes severely constrain the simultaneous estimation of their weights in the utility function. Despite the data limitations, it is found that, the ALMF algorithm can provide stable estimates of the choice parameters for some periods of the day. Finally, it is found that the daily variation of the user sensitivities for different periods of the day resembles a well-defined normal distribution.

Benthic Macrophyte Distribution and Abundance in Estuarine Mangrove Lakes and Estuaries: Relationships to Environmental Variables

Annual mean salinity, light availability, and sediment depth to bedrock structured the submerged aquatic vegetation (SAV) communities in subtropical mangrove-lined estuaries. Three distinct SAV communities (i.e., Chara group, Halodule group, and Low SAV coverage group) were identified along the Everglades–Florida Bay ecotone and related to water quality using a discriminant function model that predicted the type of plant community at a given site from salinity, light availability, and sediment depth to bedrock. Mean salinity alone was able to correctly classify 78% of the sites and reliably separated the Chara group from the Halodule group. The addition of light availability and sediment depth to bedrock increased model accuracy to 90% and further distinguished the Chara group from the Halodule group. Light availability was uniquely valuable in separating the Chara group from the Low SAV coverage group. Regression analyses identified significant relationships between phosphorus concentration, phytoplankton abundance, and light availability and suggest that a decline in water transparency, associated with increasing salinity, may have also contributed to the historical decline of Chara communities in the region. This investigation applies relationships between environmental variables and SAV distribution and provides a case study into the application of these general principals to ecosystem management.

Hazard mitigation element quality in coastal comprehensive plans in a state with strong requirements for hazard mitigation plan elements

This dissertation examines the quality of hazard mitigation elements in a coastal, hazard prone state. I answer two questions. First, in a state with a strong mandate for hazard mitigation elements in comprehensive plans, does plan quality differ among county governments? Second, if such variation exists, what drives this variation? My research focuses primarily on Florida's 35 coastal counties, which are all at risk for hurricane and flood hazards, and all fall under Florida's mandate to have a comprehensive plan that includes a hazard mitigation element. Research methods included document review to rate the hazard mitigation elements of all 35 coastal county plans and subsequent analysis against demographic and hazard history factors. Following this, I conducted an electronic, nationwide survey of planning professionals and academics, informed by interviews of planning leaders in Florida counties. I found that hazard mitigation element quality varied widely among the 35 Florida coastal counties, but were close to a normal distribution. No plans were of exceptionally high quality. Overall, historical hazard effects did not correlate with hazard mitigation element quality, but some demographic variables that are associated with urban populations did. The variance in hazard mitigation element quality indicates that while state law may mandate, and even prescribe, hazard mitigation in local comprehensive plans, not all plans will result in equal, or even adequate, protection for people. Furthermore, the mixed correlations with demographic variables representing social and disaster vulnerability shows that, at least at the county level, vulnerability to hazards does not have a strong effect on hazard mitigation element quality. From a theory perspective, my research is significant because it compares assumptions about vulnerability based on hazard history and demographics to plan quality. The only vulnerability-related variables that appeared to correlate, and at that mildly so, with hazard mitigation element quality, were those typically representing more urban areas. In terms of the theory of Neo-Institutionalism and theories related to learning organizations, my research shows that planning departments appear to have set norms and rules of operating that preclude both significant public involvement and learning from prior hazard events.

A Modified Resource Distribution Fairness Measure

An important issue of resource distribution is the fairness of the distribution. For example, computer network management wishes to distribute network resource fairly to its users. To describe the fairness of the resource distribution, a quantitative fairness score function was proposed in 1984 by Jain et al. The purpose of this paper is to propose a modified network sharing fairness function so that the users can be treated differently according to their priority levels. The mathematical properties are discussed. The proposed fairness score function keeps all the nice properties of and provides better performance when the network users have different priority levels.

Areal and vertical distribution of total soil mercury and total phosphorusin the southern half of water conservation area 3-A, Everglades, Southern Florida

Total soil-mercury and phosphorus concentrations were determined in 64 sites in the southern half of Water Conservation Area 3A, an area of approximately 500 km2 . Surface soil-Hg concentrations ranged from 117 to 300 ng-g-1;total phosphorus concentrations range from 350 to 850 pg~g-1. No consistent north-south or east-west trends are found in the mercury or phosphorus surface concentrations when they are normalized to soil bulk density. Nine sites were used for the determination of the vertical distribution of soilmercury. Vertical profiles of soil-Hg revealed decreasing concentrations with depth and correlated well with phosphorus in soil profiles. Mercury concentrations in soil profiles may be interpreted as an increase in the rate of deposition of mercury in the region in recent decades and/or as postdepositionalmobilization of mercury to surface layers.

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Spatial and Temporal Patterns in the Distribution, Behavior, and Activity of Fishes in Canals of the Everglades

Landscape characteristics, disturbances, and temporal variability influence predator-prey relationships, but are often overlooked in experimental studies. In the Everglades, seasonal disturbances force the spatial overlap of predators and prey, potentially increasing predation risk for prey. This study examined seasonal and diel patterns of fish use of canals and assessed predation risk for small fishes using an encounter rate model. I deployed an imaging sonar in Everglades canals to quantify density and swimming speeds of fishes, and detect anti-predator behaviors by small fishes. Generally, seasonal declines of marsh water-levels increased the density of large fishes in canals. Densities of small and large fishes were positively correlated and, as small-fish density increased, schooling frequency also increased. At night, schools disbanded and small fishes were observed congregating along the canal edge. The encounter rate model predicted highest predator-prey encounters during the day, but access to cover may reduce predation risk for small fishes.

Hazard Mitigation Element Quality in Coastal Comprehensive Plans in a State with Strong Requirements for Hazard Mitigation Plan Elements

This dissertation examines the quality of hazard mitigation elements in a coastal, hazard prone state. I answer two questions. First, in a state with a strong mandate for hazard mitigation elements in comprehensive plans, does plan quality differ among county governments? Second, if such variation exists, what drives this variation? My research focuses primarily on Florida’s 35 coastal counties, which are all at risk for hurricane and flood hazards, and all fall under Florida’s mandate to have a comprehensive plan that includes a hazard mitigation element. Research methods included document review to rate the hazard mitigation elements of all 35 coastal county plans and subsequent analysis against demographic and hazard history factors. Following this, I conducted an electronic, nationwide survey of planning professionals and academics, informed by interviews of planning leaders in Florida counties. I found that hazard mitigation element quality varied widely among the 35 Florida coastal counties, but were close to a normal distribution. No plans were of exceptionally high quality. Overall, historical hazard effects did not correlate with hazard mitigation element quality, but some demographic variables that are associated with urban populations did. The variance in hazard mitigation element quality indicates that while state law may mandate, and even prescribe, hazard mitigation in local comprehensive plans, not all plans will result in equal, or even adequate, protection for people. Furthermore, the mixed correlations with demographic variables representing social and disaster vulnerability shows that, at least at the county level, vulnerability to hazards does not have a strong effect on hazard mitigation element quality. From a theory perspective, my research is significant because it compares assumptions about vulnerability based on hazard history and demographics to plan quality. The only vulnerability-related variables that appeared to correlate, and at that mildly so, with hazard mitigation element quality, were those typically representing more urban areas. In terms of the theory of Neo-Institutionalism and theories related to learning organizations, my research shows that planning departments appear to have set norms and rules of operating that preclude both significant public involvement and learning from prior hazard events.