Anna K. Panorska

Parameter Estimation for the Truncated Pareto Distribution

The Pareto distribution is a simple model for nonnegative data with a power law probability tail. In many practical applications, there is a natural upper bound that truncates the probability tail. This article derives estimators for the truncated Pareto distribution, investigates their properties, and illustrates a way to check for fit. These methods are illustrated with applications from finance, hydrology, and atmospheric science.

The global distribution of diet breadth in insect herbivores

Significance Dietary specialization determines an organism’s resource base as well as impacts on host or prey species. There are important basic and applied reasons to ask why some animals have narrow diets and others are more generalized, and if different regions of the Earth support more specialized interactions. We investigated site-specific host records for more than 7,500 species of insect herbivores. Although host specialists predominate, the proportion of specialists is affected by the diversity of hosts and shifts globally, supporting predictions of more exclusive tropical interactions. These results not only affect our understanding of the ecology of food webs, but also have implications for how they respond to environmental change, as well as for ecosystem management and restoration. Understanding variation in resource specialization is important for progress on issues that include coevolution, community assembly, ecosystem processes, and the latitudinal gradient of species richness. Herbivorous insects are useful models for studying resource specialization, and the interaction between plants and herbivorous insects is one of the most common and consequential ecological associations on the planet. However, uncertainty persists regarding fundamental features of herbivore diet breadth, including its relationship to latitude and plant species richness. Here, we use a global dataset to investigate host range for over 7,500 insect herbivore species covering a wide taxonomic breadth and interacting with more than 2,000 species of plants in 165 families. We ask whether relatively specialized and generalized herbivores represent a dichotomy rather than a continuum from few to many host families and species attacked and whether diet breadth changes with increasing plant species richness toward the tropics. Across geographic regions and taxonomic subsets of the data, we find that the distribution of diet breadth is fit well by a discrete, truncated Pareto power law characterized by the predominance of specialized herbivores and a long, thin tail of more generalized species. Both the taxonomic and phylogenetic distributions of diet breadth shift globally with latitude, consistent with a higher frequency of specialized insects in tropical regions. We also find that more diverse lineages of plants support assemblages of relatively more specialized herbivores and that the global distribution of plant diversity contributes to but does not fully explain the latitudinal gradient in insect herbivore specialization.

Testing Exponentiality Versus Pareto Distribution via Likelihood Ratio

We consider the problem of maximum likelihood estimation of the parameters of the Pareto Type II (Lomax) distribution. We show that in certain parametrization and after modification of the parameter space to include exponential distribution as a special case, the MLEs of parameters always exist. Moreover, the MLEs have a non standard asymptotic distribution in the exponential case due to the lack of regularity. Further, we develop a likelihood ratio test for exponentiality versus Pareto II distribution. We emphasize that this problem is non standard, and the limiting null distribution of the deviance statistic in not chi-square. We derive relevant asymptotic theory as well as a convenient computational formula for the critical values for the test. An empirical power study and power comparisons with other tests are also provided. A problem from climatology involving precipitation data from hundreds of meteorological stations across North America provides a motivation for and an illustration of the new test.

The probability distribution of intense daily precipitation

The probability tail structure of over 22,000 weather stations globally is examined in order to identify the physically and mathematically consistent distribution type for modeling the probability of intense daily precipitation and extremes. Results indicate that when aggregating data annually, most locations are to be considered heavy tailed with statistical significance. When aggregating data by season, it becomes evident that the thickness of the probability tail is related to the variability in precipitation causing events and thus that the fundamental cause of precipitation volatility is weather diversity. These results have both theoretical and practical implications for the modeling of high-frequency climate variability worldwide.

Comparison of contrast-enhanced with non-contrast endosonography in the diagnostics of anal fistulas

The objective of this paper is to compare the accuracy of standard, non-contrast endosonography (EAS) with contrast-enhanced endosonography (CE-EAS) in the diagnosis of anal fistulas. The group consisted of 126 patients (mean age: 43.1 years) with the clinical diagnosis of anal fistula. For anal endosonography, a Bruel & Kjaer unit with a 7.0-MHz transducer was used with a 3% solution of hydrogen peroxide as the contrast agent (1, 2, 3). In each case, EAS and CE-EAS diagnoses of the type and complexity of anal fistula, as well as the location of the internal opening, were determined. Results showed that CE-EAS was significantly more accurate in diagnosing the type of anal fistulas than NC-EAS (97 vs. 94%, respectively; P=02275), and in differentiating simple from complex tracks (92 vs. 75%, respectively; P<0.00001). CE-EAS was much more accurate in patients with recurrent fistulas (57 vs. 92%, respectively; P<0.00006), whereas in a subgroup of primary tracks, both methods were of comparable accuracy. Sensitivities of CE-EAS and EAS for internal opening were 89 and 65%, respectively. The conclusion of this paper is that CE-EAS significantly increases the accuracy of standard non-contrast EAS and is especially beneficial for the differentiation between simple and complex tracks.

A watershed modeling approach to streamflow reconstruction from tree-ring records

Insight into long-term changes of streamflow is critical for addressing implications of global warming for sustainable water management. To date, dendrohydrologists have employed sophisticated regression techniques to extend runoff records, but this empirical approach cannot directly test the influence of watershed factors that alter streamflow independently of climate. We designed a mechanistic watershed model to calculate streamflows at annual timescales using as few inputs as possible. The model was calibrated for upper reaches of the Walker River, which straddles the boundary between the Sierra Nevada of California and the Great Basin of Nevada. Even though the model incorporated simplified relationships between precipitation and other components of the hydrologic cycle, it predicted water year streamflows with correlations of 0.87 when appropriate precipitation values were used.

Prevalence of Chronic Venous Disorders Among Employees Working in Prolonged Sitting and Standing Postures

Research was conducted to determine the prevalence and severity of chronic venous disorders (CVD) among people working in prolonged sitting or static standing postures. Clinical examination and duplex Doppler sonography were performed on 126 employees working in a sitting (96 individuals) or a standing posture (30 individuals). Evidence of CVD was found in 59.4% of individuals working in a sitting posture and in 83.4% of those working in a standing posture, and was significantly higher in employees working in a standing posture (p = .015). Incompetent perforating veins and vena saphena magna valves, and bilateral changes were the more frequent signs of CVD. The investigation showed that prolonged standing and sitting at work increases risk of developing CVD. Further, people working in a standing posture are at a significantly greater risk for CVD than those working in a prolonged sitting posture. They should thus be the subject of specific prophylaxis interventions.

From Diversity to Volatility: Probability of Daily Precipitation Extremes

A sensible stochastic model is required to correctly estimate the risk associated with daily precipitation extremes. The same requirement holds for studying high-frequency precipitation extremes in the context of climate variability and change. Results derived from probability theory were used to develop an efficient automated scheme to distinguish between heavy and exponential precipitation probability density function (PDF) tails in hundreds of daily station records spanning five decades over the North American continent. These results suggest that, at a vast majority of the stations, daily extreme precipitation probabilities do not decay exponentially, but more closely follow a power law. This means that statistical distributions traditionally used to model daily rainfall (e.g. exponential, Weibull, Gamma, lognormal) generally underestimate the probabilities of extremes. The degree of this distortion, i.e. volatility, depends on regional and seasonal climatic peculiarities. By examining geographical and seasonal patterns in extreme precipitation behavior, the authors show that the degree of volatility is determined regionally by the diversity in precipitation-producing mechanisms, or storm type diversity. Exponential tails are geographically limited to regions where precipitation falls almost exclusively from similar meteorological systems and where light probability tails are observed in all seasons. Topography plays an important role in flattening or fattening PDF tails by limiting the spatial extent of certain systems while orographically altering their precipitation amounts. Results presented here represent the first logical step towards choosing appropriate PDFs at various locations by specifying their regionally relevant family. Heavy tailed models are generally superior to those from the exponential family and can lead to more realistic estimates of extreme event probabilities, return periods, n-year events, and design limits. The correct choice of PDF is essential to safe engineering design, hazard assessment and other applications, as well as for fostering further investigations of hydrologic weather extremes and climate.

A Mixed Bivariate Distribution Connected with Geometric Maxima of Exponential Variables

We study the joint distribution of X and N, where N has a geometric distribution and X is the maximum of N i.i.d. exponential variables, independent of N. We present basic properties of these mixed bivariate distributions and discuss parameter estimation for this model. An example from finance, where N represents the number of consecutive positive daily log-returns of currency exchange rates, illustrates stochastic modeling potential of these laws.

Testing symmetry under a skew Laplace model

Abstract We develop tests of hypothesis about symmetry based on samples from possibly asymmetric Laplace distributions and present exact and limiting distribution of the test statistics. We postulate that the test statistic derived under the Laplace model is a rational choice as a measure of skewness and can be used in testing symmetry for other, quite general classes of skew distributions. Our results are applied to foreign exchange rates for 15 currencies.