Distribution Shape Parameter Research Articles

Estimating the amount of WEEE generated in South Korea by using the population balance model

We estimated the amount of waste electrical and electronic equipment (WEEE) generated in South Korea by using the population balance model (PBM) based on a lifespan distribution analysis. This is the first study to apply PBM to estimate WEEE generation in South Korea. The lifespan distribution analysis of electrical and electronic equipment (EEE) was based on the results of a questionnaire survey of 1000 households, which were analyzed with the Weibull distribution. As a result, we could estimate the domestic service lifespan and lifespan distribution shape parameter for eight selected products. Using the lifespan distribution analysis and other data, such as the shipment volume and the number of products owned by households, we estimated the amount of WEEE generated for the eight selected items from 2000 to 2020. We found that 1.2million air conditioners, 2.5million televisions, 1.3million microwave ovens, 1.2million kimchi refrigerators, 17.0million mobile phones, 1.7million refrigerators, 2.0million vacuum cleaners, and 1.4million washing machines were generated as WEEE in 2010. We also compared our WEEE estimates with the number of items collected through the official WEEE recycling program from 2003 to 2009 and found that in 2009 washing machines had the highest collection rate (28%) and air conditioners had the lowest rate (7%).

Spatio-temporal variation and statistical characteristic of extreme dry spell in Yellow River Basin, China

Drought is one of the most detrimental natural hazards in Yellow River Basin (YRB). In this research, spatio-temporal variation and statistical characteristic of drought in YRB is studied by using dry spell. Two extreme series, including annual maximum series (AMS) and partial duration series (PDS), are used and simulated with generalized extreme value (GEV), generalized Pareto (GP), and Pearson type III (PE3) distributions. The results show that the northern part is drier than the southern part of YRB. Besides, the maximum dry spell usually starts in October, November, and December. According to the trend analysis, mean maximum length of dry spell (MxDS) shows a negative trend in most stations. From the L-moments and Kolmogorov–Smirnov test method, it can be found that GEV model can better fit AMS while GP and PE3 can better fit PDS. Moreover, the quantiles from optimal model of AMS and PDS depict a similar distribution with values increases from south to north. The spatial distribution of scale and location parameters of GEV model for AMS shows a south-to-north gradient, while the distribution of shape parameter is a little irregularity. Furthermore, based on the linear correlation analysis, there is an evident linear relation between location and scale parameters with mean and standard variation of MxDS, respectively.

Improved Birnbaum–Saunders inference under type II censoring

The Birnbaum–Saunders distribution is useful for modeling reliability data. In this paper we obtain adjusted profile maximum likelihood estimators for the Birnbaum–Saunders distribution shape parameter under type II data censoring. We consider the adjustments to the profile likelihood function proposed by Barndorff-Nielsen (1983), Cox and Reid (1987), Fraser and Reid (1995), Fraser et al. (1999) and Severini (1998, 1999). We obtain modified profile likelihood ratio tests and also consider bootstrap-based inference. Interval estimation is addressed as well. Several bootstrap confidence intervals are considered. Monte Carlo simulation results on point estimation, interval estimation and hypothesis testing inference are reported. Finally, we present two applications that use real (not simulated) data.

Tracer design for magnetic particle imaging (invited)

Magnetic particle imaging (MPI) uses safe iron oxide nanoparticle tracers to offer fundamentally new capabilities for medical imaging, in applications as vascular imaging and ultra-sensitive cancer therapeutics. MPI is perhaps the first medical imaging platform to intrinsically exploit nanoscale material properties. MPI tracers contain magnetic nanoparticles whose tunable, size-dependent magnetic properties can be optimized by selecting a particular particle size and narrow size-distribution. In this paper we present experimental MPI measurements acquired using a homemade MPI magnetometer: a zero-dimensional MPI imaging system designed to characterize tracer performance by measuring the derivative of the time-varying tracer magnetization, M'(H(t)), at a driving frequency of 25 kHz. We show that MPI performance is optimized by selecting phase-pure magnetite tracers of a particular size and narrow size distribution; in this work, tracers with 20 nm median diameter, log-normal distribution shape parameter, σ(v), equal to 0.26, and hydrodynamic diameter equal to 30 nm showed the best performance. Furthermore, these optimized MPI tracers show 4 × greater signal intensity (measured at the third harmonic) and 20% better spatial resolution compared with commercial nanoparticles developed for MRI.

Comparison of Two Methods Used to Model Shape Parameters of Pareto Distributions

Two methods are compared for estimating the shape parameters of Pareto field-size (or pool-size) distributions for petroleum resource assessment. Both methods assume mature exploration in which most of the larger fields have been discovered. Both methods use the sizes of larger discovered fields to estimate the numbers and sizes of smaller fields: (1) the tail-truncated method uses a plot of field size versus size rank, and (2) the log–geometric method uses data binned in field-size classes and the ratios of adjacent bin counts. Simulation experiments were conducted using discovered oil and gas pool-size distributions from four petroleum systems in Alberta, Canada and using Pareto distributions generated by Monte Carlo simulation. The estimates of the shape parameters of the Pareto distributions, calculated by both the tail-truncated and log–geometric methods, generally stabilize where discovered pool numbers are greater than 100. However, with fewer than 100 discoveries, these estimates can vary greatly with each new discovery. The estimated shape parameters of the tail-truncated method are more stable and larger than those of the log–geometric method where the number of discovered pools is more than 100. Both methods, however, tend to underestimate the shape parameter. Monte Carlo simulation was also used to create sequences of discovered pool sizes by sampling from a Pareto distribution with a discovery process model using a defined exploration efficiency (in order to show how biased the sampling was in favor of larger fields being discovered first). A higher (more biased) exploration efficiency gives better estimates of the Pareto shape parameters.

On the Performance Analysis of Multi-Hop Cooperative Relay Networks over Generalized-K Fading Channels

This letter analyzes an amplify-and-forward (AF) transmission based multi-hop cooperative relay network (MCRN) over Generalized-K fading channels. In this letter, highly simplified, novel asymptotic expressions for the average symbol error rate and the outage probability of MCRNs over Generalized-K fading channels (with arbitrary fading parameters) are presented. Both theoretical analysis and simulations explicitly reveal that for MCRNs over Generalized-K fading channels, a diversity order of 2k is achieved when shadowing is more severe than fading and a diversity order of 2m is achieved when fading is more severe than shadowing (where k and m represent the Generalized-K distribution shape parameters).

Columnar aerosol optical properties in the Po Valley, Italy, from MFRSR data

The Po Valley is one of the most polluted areas in Europe. In order to provide a further contribution to the characterization of aerosol optical properties in this area, a more than 2 yr set of Multi Filter Rotating Shadow‐band Radiometer (MFRSR) measurements performed from September 2006 to May 2009 at Bologna, in northern Italy, were analyzed, paying particular attention to calibration, cloud screening, and uncertainty assessment of the measurements. The results show that daily mean aerosol optical depth (AOD) at 500 nm varies between 0.02 and 0.78, with an overall average value of 0.20 ± 0.11, and that daily mean values of Ångström's exponent α range between 0.21 and 1.86, with an overall average value of 1.23 ± 0.30. The annual variations of these parameters are evidence of the large variability of aerosol content and size distribution shape parameters throughout the year. Interannual seasonal statistics show a cyclic behavior of AOD, with monthly median values increasing from winter to autumn. In late spring and summer, several episodes of Saharan dust transport from North Africa were associated with high values of AOD and low values of α, contributing to an appreciable modification of the seasonal mean values of these two optical parameters. The high temporal resolution of daily field measurements allowed the definition of the average features of daily cycles for both parameters AOD and α, on a seasonal basis. Comparison of MFRSR results with those obtained from three AERONET stations in the Po Valley shows good agreement for both optical parameters. Absolute values of biases and root‐mean‐square differences between the MFRSR results and those of the AERONET stations were found to be lower than 0.05 and 0.20, respectively, for AOD at 500 nm and lower than 0.30 and 0.44 for α, indicating that aerosol optical characteristics are quite homogeneous over the whole region.

Modeling the Effect of Seafloor Ripples on Synthetic Aperture Sonar Speckle Statistics

The characterization and modeling of synthetic aperture sonar (SAS) image statistics is of importance for developing target-on-background detection and classification algorithms and for developing specialized filters for speckle noise reduction. In this paper, we present a model to predict the impact of amplitude scaling caused by seafloor ripples on SAS image speckle statistics. The continuous variation in scattering strength produced by ripples (i.e., ripple-induced changes in seafloor slope) is treated as deterministic amplitude scaling on image speckle produced by the SAS imaging process. Changes in image statistics caused by ripples are quantified in terms of an effective -distribution shape parameter. Agreement between shape parameter estimated from the scaling model and from SAS data collected in experiments off Panama City, FL and off the Ligurian coast near La Spezia, Italy illustrate the efficacy of the model.

The Impact of Multipath on High-Resolution SAS Image Statistics

As with traditional sonar, synthetic aperture sonar (SAS) is susceptible to multipath contamination, reducing the quality and also modifying the statistics of the image. Such multipath contaminants may either be environmentally induced, as is often the case when attempting to image ranges greater than the water depth resulting in returns from the boundaries, or may be induced by the system's supporting structure itself. A clear understanding of such statistical impact is necessary to advance synthetic aperture formation algorithms and for predicting system performance. Broadband acoustic data suitable for SAS processing collected with a rail-mounted mobile-tower as part of the U.S. Office of Naval Research (ONR)-funded Sediment Acoustics eXperiment 2004 (SAX04) are analyzed in this paper. Analysis focused on both system structure and environmentally induced multipath using the K -distribution shape parameter as a metric. High-resolution sonar imagery often exhibited significantly non-Rayleigh, heavy-tailed envelope statistics, characterized by a low equivalent K-distribution shape parameter. Analysis showed a clear and significant increase in the estimated shape parameter in the presence of multipath, representing a trend toward a Rayleigh-distributed envelope. A model for reverberation is presented to provide bounds of the statistical impact using observable image intensity level increases in synthetic-aperture-formed images caused by multipath contamination. This model further shows potential for statistical impact when multipath arrivals are of similar level as the direct path even when not observable in the image (e.g., within 10 dB).

Is there variation in crossover interference levels among chromosomes from human males?

We demonstrate that recent data from human males are consistent with constant interference levels among chromosomes under the two-pathway model, whereas inappropriately fitting shape parameters of Gamma distributions to immunofluorescent interfoci distances observed on finite chromosomes generates false interpretations of higher levels of interference on shorter chromosomes. We provide appropriate statistical methodology.

How Do Variable Substitution Rates Influence Ka and Ks Calculations?

The ratio of nonsynonymous substitution rate (Ka) to synonymous substitution rate (Ks) is widely used as an indicator of selective pressure at sequence level among different species, and diverse mutation models have been incorporated into several computing methods. We have previously developed a new γ-MYN method by capturing a key dynamic evolution trait of DNA nucleotide sequences, in consideration of varying mutation rates across sites. We now report a further improvement of NG, LWL, MLWL, LPB, MLPB, and YN methods based on an introduction of gamma distribution to illustrate the variation of raw mutation rate over sites. The novelty comes in two ways: (1) we incorporate an optimal gamma distribution shape parameter a into γ-NG, γ-LWL, γ-MLWL, γ-LPB, γ-MLPB, and γ-YN methods; (2) we investigate how variable substitution rates affect the methods that adopt different models as well as the interplay among four evolutional features with respect to Ka/Ks computations. Our results suggest that variable substitution rates over sites under negative selection exhibit an opposite effect on ω estimates compared with those under positive selection. We believe that the sensitivity of our new methods has been improved than that of their original methods under diverse conditions and it is advantageous to introduce novel parameters for Ka/Ks computation.

Are mergers responsible for universal halo properties?

N-body simulations of cold dark matter (CDM) have shown that, in this hierarchical structure formation model, dark matter halo properties, such as the density profile, the phase-space density profile, the distribution of axial ratio, the distribution of spin parameter and the distribution of internal specific angular momentum, follow ‘universal’ laws or distributions. Here, we study the properties of the first generation of haloes in a hot dark matter (HDM) dominated universe, as an example of halo formation through monolithic collapse. We find all these universalities to be present in this case also. Halo density profiles are very well fit by the Navarro, Frenk & White profile over two orders of magnitude in mass. The concentration parameter depends on mass as c∝M0.2, reversing the dependence found in a hierarchical CDM universe. However, the concentration–formation time relation is similar in the two cases: earlier forming haloes tend to be more concentrated than their later forming counterparts. Halo formation histories are also characterized by two phases in the HDM case: an early phase of rapid accretion followed by slower growth. Furthermore, there is no significant difference between the HDM and CDM cases concerning the statistics of other halo properties: the phase-space density profile; the velocity anisotropy profile; the distribution of shape parameters; the distribution of spin parameter and the distribution of internal specific angular momentum are all similar in the two cases. Only substructure content differs dramatically. These results indicate that mergers do not play a pivotal role in establishing the universalities, thus contradicting models which explain them as consequences of mergers.

Array Modeling of Active Sonar Clutter

Active sonar systems operating in shallow-water environments often deal with excessive false alarms, generically referred to as clutter, that are more numerous than expected for Rayleigh-distributed reverberation. The clutter probability density function, and therefore the probability of false alarm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> ), depends on the scattering sources, propagation conditions, sonar system, and signal processing. Clutter statistics are often approximated by the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distribution where the shape parameter (alpha macr) provides an inverse relationship to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> with decreases in alpha macr representing an increase in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> . In this paper, the effect of sonar array processing on clutter statistics is evaluated by first modeling clutter at the hydrophone level and then analyzing the resulting <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distribution shape parameter after conventional beamforming. When the transmit-waveform bandwidth is narrowband with respect to the array processing and propagation consists primarily of low-angle paths, alpha macr was found to be separable into the product of a clutter-source scattering effect, an array processing effect, and a coupled transmit-waveform and propagation effect. The array effect was found to coarsely follow the array beamwidth, although precise evaluation is straightforward given the array beampattern. As might be expected, array design or processing that tends to increase the beamwidth was found to increase alpha macr. Uniform shading was seen to provide a practical, though not exact, lower bound on alpha macr for common array shading functions. For circular arrays with unaliased spatial sampling, an asymptotic beampattern was found to provide a very accurate approximation to alpha macr. These results should be useful in predicting the performance of sonar systems in clutter dominated areas, in the design of arrays and array processing, in the inversion of clutter data for clutter-source scattering parameters, or to improve signal processing algorithms aiming to reduce or control clutter-related false alarms.

The Berry and Reinhardt Autoconversion Parameterization: A Digest

Abstract The simplified version of the Berry and Reinhardt parameterization used for initiating rain from cloud droplets is presented and is compared with 12 other versions of itself from the literature. Many of the versions that appear to be different from each other can be brought into agreement with the original parameterization by making the same assumptions: a mean diameter based upon mass or volume and distribution shape parameters chosen to give the same cloud mass relative variance as the original Berry and Reinhardt parameterization. However, there are differences in how authors have chosen to parameterize the cloud number concentration sink and rain number concentration source, and those choices, along with model limitations, have important impacts on rain development within the scheme. These differences among versions are shown to have important time-integrated feedbacks upon the developing initial rain distribution. Three of 12 implementations of the bulk scheme are shown to be able to reproduce the original Berry and Reinhardt bin-model solutions very well, and about 6 of 12 do poorly.

Evaluation of Hydrophilic Permeant Transport Parameters in the Localized and Non-Localized Transport Regions of Skin Treated Simultaneously With Low-Frequency Ultrasound and Sodium Lauryl Sulfate

The porosity (epsilon), the tortuosity (tau), and the hindrance factor (H) of the aqueous pore channels located in the localized transport regions (LTRs) and the non-LTRs formed in skin treated simultaneously with low-frequency ultrasound (US) and the surfactant sodium lauryl sulfate (SLS), were evaluated for the delivery of four hydrophilic permeants (urea, mannitol, raffinose, and inulin) by analyzing dual-radiolabeled diffusion masking experiments for three different idealized cases of the aqueous pore pathway hypothesis. When epsilon and tau were assumed to be independent of the permeant radius, H was found to be statistically larger in the LTRs than in the non-LTRs. When a distribution of pore radii was assumed to exist in the skin, no statistical differences in epsilon, tau, and H were observed due to the large variation in the pore radii distribution shape parameter (3 A to infinity). When infinitely large aqueous pores were assumed to exist in the skin, epsilon was found to be 3-8-fold greater in the LTRs than in the non-LTRs, while little difference was observed in the LTRs and in the non-LTRs for tau. This last result suggests that the efficacy of US/SLS treatment may be enhanced by increasing the porosity of the non-LTRs.

Modeling Envelope Statistics of Blood and Myocardium for Segmentation of Echocardiographic Images

The objective of this study was to investigate the use of speckle statistics as a preprocessing step for segmentation of the myocardium in echocardiographic images. Three-dimensional (3D) and biplane image sequences of the left ventricle of two healthy children and one dog (beagle) were acquired. Pixel-based speckle statistics of manually segmented blood and myocardial regions were investigated by fitting various probability density functions (pdf). The statistics of heart muscle and blood could both be optimally modeled by a K-pdf or Gamma-pdf (Kolmogorov-Smirnov goodness-of-fit test). Scale and shape parameters of both distributions could differentiate between blood and myocardium. Local estimation of these parameters was used to obtain parametric images, where window size was related to speckle size (5 × 2 speckles). Moment-based and maximum-likelihood estimators were used. Scale parameters were still able to differentiate blood from myocardium; however, smoothing of edges of anatomical structures occurred. Estimation of the shape parameter required a larger window size, leading to unacceptable blurring. Using these parameters as an input for segmentation resulted in unreliable segmentation. Adaptive mean squares filtering was then introduced using the moment-based scale parameter (σ 2/μ) of the Gamma-pdf to automatically steer the two-dimensional (2D) local filtering process. This method adequately preserved sharpness of the edges. In conclusion, a trade-off between preservation of sharpness of edges and goodness-of-fit when estimating local shape and scale parameters is evident for parametric images. For this reason, adaptive filtering outperforms parametric imaging for the segmentation of echocardiographic images. (E-mail: m.m.nillesen@cukz.umcn.nl)

Joint Inference of the Distribution of Fitness Effects of Deleterious Mutations and Population Demography Based on Nucleotide Polymorphism Frequencies

The distribution of fitness effects of new mutations (DFE) is important for addressing several questions in genetics, including the nature of quantitative variation and the evolutionary fate of small populations. Properties of the DFE can be inferred by comparing the distributions of the frequencies of segregating nucleotide polymorphisms at selected and neutral sites in a population sample, but demographic changes alter the spectrum of allele frequencies at both neutral and selected sites, so can bias estimates of the DFE if not accounted for. We have developed a maximum-likelihood approach, based on the expected allele-frequency distribution generated by transition matrix methods, to estimate parameters of the DFE while simultaneously estimating parameters of a demographic model that allows a population size change at some time in the past. We tested the method using simulations and found that it accurately recovers simulated parameter values, even if the simulated demography differs substantially from that assumed in our analysis. We use our method to estimate parameters of the DFE for amino acid-changing mutations in humans and Drosophila melanogaster. For a model of unconditionally deleterious mutations, with effects sampled from a gamma distribution, the mean estimate for the distribution shape parameter is approximately 0.2 for human populations, which implies that the DFE is strongly leptokurtic. For Drosophila populations, we estimate that the shape parameter is approximately 0.35. Differences in the shape of the distribution and the mean selection coefficient between humans and Drosophila result in significantly more strongly deleterious mutations in Drosophila than in humans, and, conversely, nearly neutral mutations are significantly less frequent.

Physical Characterization or Aerosol Emissions from a Commercial Gas Turbine Engine

This paper discusses the results of the Aircraft Particle Emissions Experiment Project for the physical characterization of total (nonvolatile plus volatile) aerosol emissions (emission factors, hydration properties, and distribution shape parameters) by extractive sampling from an on-wing CFM56-2C 1 engine. Samples were extracted at the engine exit plane (1 m) as well as locations 10 and 30 m downstream. Three different fuels were used in this study: base fuel, high-sulfur fuel, and high-aromatic fuel. For the 1 and 10-m probe locations, strong and sometimes nonlinear dependencies were observed on fuel flow rate and no statistically significant dependencies were observed for fuel composition. At 30 m, the onset of gas-to-particle conversion was apparent for low- to medium-fuel flow rates. The soluble mass fraction was found to increase with distance from the engine exit plane and with increasing fuel aromatic and sulfur content. An intercomparison of gas and particle sampling trains showed that gas-to-particle conversion is a serious sample train artifact for gas sampling trains in which dilution cannot be achieved at the probe tip.

Aerosols in polar regions: A historical overview based on optical depth and in situ observations

Large sets of filtered actinometer, filtered pyrheliometer and Sun photometer measurements have been carried out over the past 30 years by various groups at different Arctic and Antarctic sites and for different time periods. They were examined to estimate ensemble average, long‐term trends of the summer background aerosol optical depth AOD(500 nm) in the polar regions (omitting the data influenced by Arctic haze and volcanic eruptions). The trend for the Arctic was estimated to be between −1.6% and −2.0% per year over 30 years, depending on location. No significant trend was observed for Antarctica. The time patterns of AOD(500 nm) and Ångström's parameters α and β measured with Sun photometers during the last 20 years at various Arctic and Antarctic sites are also presented. They give a measure of the large variations of these parameters due to El Chichon, Pinatubo, and Cerro Hudson volcanic particles, Arctic haze episodes most frequent in winter and spring, and the transport of Asian dust and boreal smokes to the Arctic region. Evidence is also shown of marked differences between the aerosol optical parameters measured at coastal and high‐altitude sites in Antarctica. In situ optical and chemical composition parameters of aerosol particles measured at Arctic and Antarctic sites are also examined to achieve more complete information on the multimodal size distribution shape parameters and their radiative properties. A characterization of aerosol radiative parameters is also defined by plotting the daily mean values of α as a function of AOD(500 nm), separately for the two polar regions, allowing the identification of different clusters related to fifteen aerosol classes, for which the spectral values of complex refractive index and single scattering albedo were evaluated.

Stochastic downscaling of precipitation: From dry events to heavy rainfalls

Downscaling precipitation is a difficult challenge for the climate community. We propose and study a new stochastic weather typing approach to perform such a task. In addition to providing accurate small and medium precipitation, our procedure possesses built‐in features that allow us to model adequately extreme precipitation distributions. First, we propose a new distribution for local precipitation via a probability mixture model of Gamma and Generalized Pareto (GP) distributions. The latter one stems from Extreme Value Theory (EVT). The performance of this mixture is tested on real and simulated data, and also compared to classical rainfall densities. Then our downscaling method, extending the recently developed nonhomogeneous stochastic weather typing approach, is presented. It can be summarized as a three‐step program. First, regional weather precipitation patterns are constructed through a hierarchical ascending clustering method. Second, daily transitions among our precipitation patterns are represented by a nonhomogeneous Markov model influenced by large‐scale atmospheric variables like NCEP reanalyses. Third, conditionally on these regional patterns, precipitation occurrence and intensity distributions are modeled as statistical mixtures. Precipitation amplitudes are assumed to follow our mixture of Gamma and GP densities. The proposed downscaling approach is applied to 37 weather stations in Illinois and compared to various possible parameterizations and to a direct modeling. Model selection procedures show that choosing one GP distribution shape parameter per pattern for all stations provides the best rainfall representation amongst all tested models. This work highlights the importance of EVT distributions to improve the modeling and downscaling of local extreme precipitations.