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Pareto Distribution (pareto + distribution)
Selected AbstractsModeling tropical cyclone intensity with quantile regressionINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 10 2009Thomas H. Jagger Abstract Wind speeds from tropical cyclones (TCs) occurring near the USA are modeled with climate variables (covariates) using quantile regression. The influences of Atlantic sea-surface temperature (SST), the Pacific El Niño, and the North Atlantic oscillation (NAO) on near-coastal TC intensity are in the direction anticipated from previous studies using Poisson regression on cyclone counts and are, in general, strongest for higher intensity quantiles. The influence of solar activity, a new covariate, peaks near the median intensity level, but the relationship switches sign for the highest quantiles. An advantage of the quantile regression approach over a traditional parametric extreme value model is that it allows easier interpretation of model coefficients (parameters) with respect to changes to the covariates since coefficients vary as a function of quantile. It is proven mathematically that parameters of the Generalized Pareto Distribution (GPD) for extreme events can be used to estimate regression coefficients for the extreme quantiles. The mathematical relationship is demonstrated empirically using the subset of TC intensities exceeding 96 kt (49 m/s). Copyright © 2008 Royal Meteorological Society [source] The wealth of species: ecological communities, complex systems and the legacy of Frank PrestonECOLOGY LETTERS, Issue 3 2007Jeffrey C. Nekola Abstract General statistical patterns in community ecology have attracted considerable recent debate. Difficulties in discriminating among mathematical models and the ecological mechanisms underlying them are likely related to a phenomenon first described by Frank Preston. He noted that the frequency distribution of abundances among species was uncannily similar to the Boltzmann distribution of kinetic energies among gas molecules and the Pareto distribution of incomes among wage earners. We provide additional examples to show that four different ,distributions of wealth' (species abundance distributions, species,area and species,time relations, and distance decay of compositional similarity) are not unique to ecology, but have analogues in other physical, geological, economic and cultural systems. Because these appear to be general statistical patterns characteristic of many complex dynamical systems they are likely not generated by uniquely ecological mechanistic processes. [source] On the distribution of wildfire sizesENVIRONMETRICS, Issue 6 2003Frederic Paik Schoenberg Abstract A variety of models for the wildfire size distribution are examined using data on Los Angeles County wildfires greater than 100 acres between 1950 and 2000. In addition to graphs and likelihood criteria, Kolmogorov,Smirnoff and Cramer,von Mises statistics are used to compare the models. The tapered Pareto distribution appears to fit the data quite well and offers some advantages over the untapered Pareto distribution, while alternatives including the lognormal, half-normal, exponential and extremal distributions fit poorly. The size distribution appears to be quite stable over the examination period, though inspection of the transformed wildfire sizes for the tapered Pareto reveals some limited trend in the residuals, indicating a very slight gradual decrease in the average fire size in Los Angeles County over these 50 years. Copyright © 2003 John Wiley & Sons, Ltd. [source] Bootstrap simulations for evaluating the uncertainty associated with peaks-over-threshold estimates of extreme wind velocityENVIRONMETRICS, Issue 1 2003M. D. Pandey Abstract In the peaks-over-threshold (POT) method of extreme quantile estimation, the selection of a suitable threshold is critical to estimation accuracy. In practical applications, however, the threshold selection is not so obvious due to erratic variation of quantile estimates with minor changes in threshold. To address this issue, the article investigates the variation of quantile uncertainty (bias and variance) as a function of threshold using a semi-parametric bootstrap algorithm. Furthermore, the article compares the performance of L-moment and de Haan methods that are used for fitting the Pareto distribution to peak data. The analysis of simulated and actual U.S. wind speed data illustrates that the L-moment method can lead to almost unbiased quantile estimates for certain thresholds. A threshold corresponding to minimum standard error appears to provide reasonable estimates of wind speed extremes. It is concluded that the quantification of uncertainty associated with a quantile estimate is necessary for selecting a suitable threshold and estimating the design wind speed. For this purpose, semi-parametric bootstrap method has proved to be a simple, practical and effective tool. Copyright © 2003 John Wiley & Sons, Ltd. [source] Three-parameter discontinuous distributions for hydrological samples with zero valuesHYDROLOGICAL PROCESSES, Issue 15 2005Stanislaw Weglarczyk Abstract A consistent approach to the frequency analysis of hydrologic data in arid and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum-based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three-parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two-parameter generalized Pareto distribution; (3) the Dirac delta combined with two-parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM-estimated parameters showed the best fit of all the three-parameter models. Copyright © 2005 John Wiley & Sons, Ltd. [source] A new traffic model for backbone networks and its application to performance analysisINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 6 2008Ming Yu Abstract In this paper, we present a new traffic model constructed from a random number of shifting level processes (SLP) aggregated over time, in which the lengths of the active periods of the SLP are of Pareto or truncated Pareto distribution. For both cases, the model has been proved to be asymptotically second-order self-similar. However, based on extensive traffic data we collected from a backbone network, we find that the active periods of the constructing SLPs can be approximated better by a truncated Pareto distribution, instead of the Pareto distribution as assumed in existing traffic model constructions. The queueing problem of a single server fed with a traffic described by the model is equivalently converted to a problem with a traffic described by Norros' model. For the tail probability of the queue length distribution, an approximate expression and upper bound have been found in terms of large deviation estimates and are mathematically more tractable than existing results. The effectiveness of the traffic model and performance results are demonstrated by our simulations and experimental studies on a backbone network. Copyright © 2007 John Wiley & Sons, Ltd. [source] OLS ESTIMATION AND THE t TEST REVISITED IN RANK-SIZE RULE REGRESSION,JOURNAL OF REGIONAL SCIENCE, Issue 4 2008Yoshihiko Nishiyama ABSTRACT The rank-size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the t test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the t statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the t statistic explodes asymptotically even under the null, indicating that a mechanical application of the t test yields a serious type I error. To overcome this problem, critical regions of the t test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005). By using the same database as that used in Soo (2005), we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual t test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries. [source] PROBABILISTIC CHARACTERISTICS OF STRESS CHANGES DURING CEREAL SNACK PUNCTUREJOURNAL OF TEXTURE STUDIES, Issue 2 2007YOSHIKI TSUKAKOSHI ABSTRACT During puncture tests of Japanese cereal snacks, the force increases and decreases alternately. We herein compare the force,deformation curves recorded by two different testing machines and show that the number of changes in the curves depends on the testing machine. Thus, it is impossible to compare results obtained using different instruments. By removing the higher-frequency components of the force,deformation curves, small events are easily missed. The number of large events decreases when lower-frequency components are eliminated. This suggests the importance of providing the information on the frequency range of the testing machines. Nevertheless, the number of large force changes is similar between the examined machines. To model the size,frequency distribution, we selected a parametric probabilistic model from among the Weibull, exponential and Pareto distributions using Akaike information criterion and found that the Weibull or exponential distributions have a fit better than the Pareto distribution. PRACTICAL APPLICATIONS The methods developed in this work can be used to evaluate the quality of crisp snack food. By analyzing the samples obtained from a lot, samples with poor texture because of abnormal moisture levels and/or ingredients can be discerned and can be used to accept or reject the lot. [source] A Pareto model for classical systemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2008Saralees Nadarajah Abstract A new Pareto distribution is introduced for pooling knowledge about classical systems. It takes the form of the product of two Pareto probability density functions (pdfs). Various structural properties of this distribution are derived, including its cumulative distribution function (cdf), moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Copyright © 2007 John Wiley & Sons, Ltd. [source] Generalized Pareto models with application to drought dataENVIRONMETRICS, Issue 4 2008Saralees Nadarajah Abstract Generalized Pareto distributions are some of the most applied distributions in environmental sciences. In this paper, a drought application is described by deriving the exact distributions of the sum X,+,Y, the product XY, and the ratio X/(X,+,Y) when X and Y are independent generalized Pareto random variables. Drought data from the State of Nebraska are used. Copyright © 2007 John Wiley & Sons, Ltd. [source] PROBABILISTIC CHARACTERISTICS OF STRESS CHANGES DURING CEREAL SNACK PUNCTUREJOURNAL OF TEXTURE STUDIES, Issue 2 2007YOSHIKI TSUKAKOSHI ABSTRACT During puncture tests of Japanese cereal snacks, the force increases and decreases alternately. We herein compare the force,deformation curves recorded by two different testing machines and show that the number of changes in the curves depends on the testing machine. Thus, it is impossible to compare results obtained using different instruments. By removing the higher-frequency components of the force,deformation curves, small events are easily missed. The number of large events decreases when lower-frequency components are eliminated. This suggests the importance of providing the information on the frequency range of the testing machines. Nevertheless, the number of large force changes is similar between the examined machines. To model the size,frequency distribution, we selected a parametric probabilistic model from among the Weibull, exponential and Pareto distributions using Akaike information criterion and found that the Weibull or exponential distributions have a fit better than the Pareto distribution. PRACTICAL APPLICATIONS The methods developed in this work can be used to evaluate the quality of crisp snack food. By analyzing the samples obtained from a lot, samples with poor texture because of abnormal moisture levels and/or ingredients can be discerned and can be used to accept or reject the lot. [source] | |||||||||||||