Shape Parameter Of Gamma Distribution Research Articles

Vertical Profile Climatology of Polarimetric Radar Variables and Retrieved Microphysical Parameters in Synoptic and Lake Effect Snowstorms

AbstractThis study derives polarimetric radar vertical profiles and microphysical retrievals for 25 Synoptic Snow (SS) and 23 Lake Effect Snow (LES) cases using the Range‐Defined Quasi‐Vertical Profiles (RD‐QVP), Columnar Vertical Profiles (CVP), and Process‐oriented Vertical Profiles (POVP) methods. For all vertical profile techniques, SS cases exhibit a near‐linear increase in reflectivity from −30 to 0°C whereas ZDR and Kdp locally peak in the dendritic growth layer. LES cases universally exhibit negative ZDR, rather high Z, negligible Kdp, and near‐unity ρhv. Ground measurements from the past OWLeS campaign provide direct evidence that conical graupel may strongly affect these polarimetric measurements in LES bands. Aggregation efficiencies for SS cases are estimated by optimizing the theoretical number concentration (Nt) and mean volume diameter (Dm) steady‐state vertical profiles against radar‐retrieved profiles derived from 20 of the 25 synoptic storm RD‐QVPs. The median estimated aggregation efficiency is approximately 0.15 with a relatively narrow interquartile range that spans from 0.1 to just over 0.2. Values of optimized aggregation efficiencies are nearly independent of the assumed gamma distribution shape parameter. These results are used to derive temperature‐dependent, climatological steady‐state relations for vertical profiles of Nt, Dm, and liquid‐equivalent snowfall rates. These results can be used in numerical weather prediction model aggregation parameterizations and can also provide climatologically representative vertical profiles of radar and microphysical quantities.

Comparisons of Rainfall Microphysical Characteristics between the Southeastern Tibetan Plateau and Low-Altitude Areas

Abstract The low air pressure and density over the Tibetan Plateau may have an impact on the microphysical features of rainfall. Using a two-dimensional video disdrometer (2DVD), a Micro Rain Radar (MRR), and a microwave radiometer (MWR), the features of the raindrop size distribution (DSD) on the southeastern Tibetan Plateau (SETP) are explored and compared with those in low-altitude regions. The falling speed of raindrops on the SETP is higher than that in low-altitude areas. Under different rainfall-rate categories, the number concentration and the maximum diameter of raindrops on the SETP are smaller than those in low-altitude regions. The convective rainfall on the SETP is more maritime-like because the South Asian summer monsoon brings water vapor from the ocean here. For stratiform and convective rainfall, the SETP has more small-sized raindrops than low-altitude locations. The mass-weighted mean diameters (Dm) on the SETP are the smallest among six sites. The generalized intercept parameter (Nw) of stratiform rainfall is balanced at a low rainfall rate, while that of convective rainfall is balanced at a high rainfall rate. Furthermore, for a given μ (the shape parameter of gamma distribution) value, the λ (the slope parameter of gamma distribution) value on the SETP is the highest of the six sites. Significance Statement For the occurrence and progression of rainfall, microphysical processes (for instance, collision, fragmentation, coalescence, and evaporation) that take place when rainfall particles descend are crucial. A key factor in the microphysical features of rainfall that varies with rainfall rates and types is the raindrop size distribution (DSD). The southeastern Tibetan Plateau (SETP)’s unique terrain ensures that there is enough moisture for rain to fall there, but little is known about the microphysical aspects of this type of precipitation. There has not been enough research done on how the high altitude affects the microphysical features of rainfall. The microphysical features of rainfall in this area must thus be studied.

Transitions between neocortical seizure and non-seizure-like states and their association with presynaptic glutamate release

The transition between seizure and non-seizure states in neocortical epileptic networks is governed by distinct underlying dynamical processes. Based on the gamma distribution of seizure and inter-seizure durations, over time, seizures are highly likely to self-terminate; whereas, inter-seizure durations have a low chance of transitioning back into a seizure state. Yet, the chance of a state transition could be formed by multiple overlapping, unknown synaptic mechanisms. To identify the relationship between the underlying synaptic mechanisms and the chance of seizure-state transitions, we analyzed the skewed histograms of seizure durations in human intracranial EEG and seizure-like events (SLEs) in local field potential activity from mouse neocortical slices, using an objective method for seizure state classification. While seizures and SLE durations were demonstrated to have a unimodal distribution (gamma distribution shape parameter >1), suggesting a high likelihood of terminating, inter-SLE intervals were shown to have an asymptotic exponential distribution (gamma distribution shape parameter <1), suggesting lower probability of cessation. Then, to test cellular mechanisms for these distributions, we studied the modulation of synaptic neurotransmission during, and between, the in vitro SLEs. Using simultaneous local field potential and whole-cell voltage clamp recordings, we found a suppression of presynaptic glutamate release at SLE termination, as demonstrated by electrically- and optogenetically-evoked excitatory postsynaptic currents (EPSCs), and focal hypertonic sucrose application. Adenosine A1 receptor blockade interfered with the suppression of this release, changing the inter-SLE shape parameter from asymptotic exponential to unimodal, altering the chance of state transition occurrence with time. These findings reveal a critical role for presynaptic glutamate release in determining the chance of neocortical seizure state transitions.

Some mitochondrial genes perform better for damselfly phylogenetics: species‐ and population‐level analyses of four complete mitogenomes of Euphaea sibling species

AbstractAnimal mitochondrial genes continue to provide an efficient and inexpensive assessment of genetic diversity. However, which mitochondrial genes should be selected to best estimate species phylogeny and population genealogy remains uncertain for most under‐sampled taxa. We analysed four complete mitochondrial genomes of sibling species of Euphaea damselflies, E. decorata, E. ornata, E. formosa and E. yayeyamana (Insecta, Odonata, Euphaeidae), to examine the patterns of selection and to evaluate the phylogenetic utility of the mitochondrial genes compared with nuclear genes. The results indicated that mitochondrial protein‐coding nad2 (NADH dehydrogenase subunit 2) and noncoding A + T‐rich (control region) genes have the highest mutation rates and more phylogenetic utility [higher parsimony‐informative sites; higher α (the shape parameter of gamma distribution); lower rates of heterogeneity among sites; and higher relative substitution rates] than all the other mitochondrial and nuclear genes analysed. In contrast, the animal DNA barcoding gene cytochrome c oxidase subunit 1 (cox1) had average values for all estimated parameters of phylogenetic performance and was sometimes outperformed by other mitochondrial genes. The majority of the mitochondrial and nuclear genes in Euphaea damselflies have experienced frequent purifying selection, except for two cases of potential positive selection in NADH dehydrogenase subunit 3 (nad3) and elongation factor 1α (EF1α), and all mitochondrial genes had experienced stronger purifying selection than nuclear genes. Our findings indicated that mitochondrial nad2 and the A + T‐rich region should be selected to provide efficient and high‐resolution phylogenetic markers for damselflies at the species and population level.

SPARSE BAYESIAN LEARNING BOOSTED BY PARTIAL ERRONEOUS SUPPORT KNOWLEDGE.

Recovery of sparse signals with unknown clustering pattern in the case of having partial erroneous prior knowledge on the supports of the signal is considered. In this case, we provide a modified sparse Bayesian learning model to incorporate prior knowledge and simultaneously learn the unknown clustering pattern. For this purpose, we add one more layer to support-aided sparse Bayesian learning algorithm (SA-SBL). This layer adds a prior on the shape parameters of Gamma distributions, those modeled to account for the precision of the solution elements. We make the shape parameters depend on the total variations on the estimated supports of the solution. Based on the simulation results, we show that the proposed algorithm is able to modify its erroneous prior knowledge on the supports of the solution and learn the clustering pattern of the true signal by filtering out the incorrect supports from the estimated support set.

Estimation Based on Likelihood Depth with Application to the Shape Parameter of Gamma Distribution

Estimation Based on Likelihood Depth with Application to the Shape Parameter of Gamma Distribution

A note on comparison and improvement of estimators based on likelihood

The problem of estimation of a parameter of interest in the presence of a nuisance parameter, which is either location or scale, is considered. Three estimators are taken into account: usual maximum likelihood (ML) estimator, maximum integrated likelihood estimator and the bias-corrected ML estimator. General results on comparison of these estimators w.r.t. the second-order risk based on the mean-squared error are obtained. Possible improvements of basic estimators via the notion of admissibility and methodology given in Ghosh and Sinha [A necessary and sufficient condition for second order admissibility with applications to Berkson's bioassay problem. Ann Stat. 1981;9(6):1334–1338] are considered. In the recent paper by Tanaka et al. [On improved estimation of a gamma shape parameter. Statistics. 2014; doi:10.1080/02331888.2014.915842], this problem was considered for estimating the shape parameter of gamma distribution. Here, we perform more accurate comparison of estimators for this case as well as for some other cases.

A method for solving relative dispersion of the cloud droplet spectra

The relative dispersion of the cloud droplet spectra or the shape parameter is usually assumed to be a constant in the two-parameter cloud microphysical scheme, or is derived through statistical analysis. However, observations have revealed that the use of such methods is not applicable for all actual cases. In this study, formulas were derived based on cloud microphysics and the properties of gamma function to solve the average cloud droplet radius and the cloud droplet spectral shape parameter. The gamma distribution shape parameter, relative dispersion, and cloud droplet spectral distribution can be derived through solving the droplet spectral shape parameter equation using the average droplet radius, volume radius, and their ratio, thereby deriving an analytic solution. We further examined the equation for the droplet spectral shape parameter using the observational droplet spectral data, and results revealed the feasibility of the method. In addition, when the method was applied to the two-parameter cloud microphysical scheme of the Weather Research and Forecast (WRF) model to further examine its feasibility, the modeling results showed that it improved precipitation simulation performance, thereby indicating that it can be utilized in two-parameter cloud microphysical schemes.

Small Sample Tests for Shape Parameters of Gamma Distributions

The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many independent gamma populations, one may test equality (or homogeneity) of shape parameters. In this article, we develop two tests for testing shape parameters of gamma distributions using chi-square distributions, stochastic majorization, and Schur convexity. The first one tests hypotheses on the shape parameter of a single gamma distribution. We numerically examine the performance of this test and find that it controls Type I error rate for small samples. To compare shape parameters of a set of independent gamma populations, we develop a test that is unbiased in the sense of Schur convexity. These tests are motivated by the need to have simple, easy to use tests and accurate procedures in case of small samples. We illustrate the new tests using three real datasets taken from engineering and environmental science. In addition, we investigate the Bayes’ factor in this context and conclude that for small samples, the frequentist approach performs better than the Bayesian approach.

Superstatistical fluctuations in time series of leverage returns

We analyze to what extent the emergence of fat-tailed q-Gaussian distributions of daily leverage returns of North American industrial companies that survive default and de-listing between 2006 and 2012 can be described by superstatistics. To this end, we compare mean values of the Tsallis entropic parameter q obtained by two independent methods: (i) direct fitting of q-Gaussians to distributions of leverage returns; and (ii) derived from shape parameters of Gamma distributions fitted to histograms of inverted realized variances of these returns. For a vast majority of companies, we observe the striking consistency of average values of q obtained by both methods. This finding supports the applicability of superstatistical hypothesis, which assumes that q-Gaussians result from the superposition of locally normal distributions with Gamma-distributed precision (inverted variance).

Superstatistical Fluctuations in Time Series of Leverage Returns

Fat tails of q-Gaussian distributions of daily log-leverage-returns of 520 North American industrial firms reported by Katz and Tian (2013) imply a significantly higher credit risk at short time-horizons and/or large initial distances to the default barrier than forecasted by traditional structural models. Superstatistics can explain the origin of this behavior and allows for a straightforward generalization of conventional models of default. Here, we verify manifestation of these distributions with Kolmogorov-Smirnov test and analyze to what extent emergence of q-Gaussians can be described by superstatistics. To this end, we compare mean values of the Tsallis entropic parameter q obtained by two independent methods: i) direct fitting of q-Gaussians to distributions of log-leverage-returns and ii) derived from shape parameters of Gamma distributions fitted to histograms of inversed realized variances of these returns. For a vast majority of companies, we observe the striking consistency of the average values of q, converging to 1.47, obtained by both methods. This finding supports the applicability of superstatistical hypothesis, which assumes that q-Gaussians result from locally normal fluctuations with Gamma-distributed precision. Notably, for a small group of firms (~8%) having distributions with divergent second moment, the mean values of q derived by both methods are very different. It is likely that in this group of issuers, fluctuations of daily log-leverage-returns are so violent that the superstatistical model assumptions are not applicable. These findings are important for practical implementations of credit risk valuations and pricing of credit securities.

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.

1444 セラミックスの欠陥寸法原分布のパラメータの破壊強度に及ぼす影響(S07-1 セラミックスおよびセラミックス系複合材料I,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

In this report, gamma distribution is used for flaw size distribution, and their parameters are estimated by the most likelihood method by using the flaw size data reported by Nakamura et.al. Taking the logarithms of its probability density function, a term in proportion to the flaw size is several orders of magnitude larger than the other terms. Therefore, linearization of flaw size distribution can be made by neglecting the other terms. To compare the experimental data, the gamma distribution parameters are used for the linearization, so this parameter expresses the character of flaw size distribution well. To consider about the relation between the fracture strength and flaw size distribution, the fracture strength and the shape parameter of gamma distribution are discussed.

Settling velocity of the suspended sediment in three high-energy environments

The in situ distribution by weight of the suspended sediment is studied in terms of settling velocity. The available published data concerning this distribution in three high-energy regions (San Francisco Bay, Thames estuary and Loire estuary) is in good accordance with a gamma distributed settling velocity. The vertical dynamics of the suspended aggregates in a flow is examined under steady state conditions. As a consequence of this dynamics, if the settling velocity of the suspended sediment mass at the bottom is gamma distributed, then, settling velocity is gamma distributed at every level z in the water column. In this case the vertical variation of the local mean settling velocity W ¯ is proportional to a power 1/ r of the local concentration C, where r is the gamma distribution shape parameter.

Estimation of WGEN weather generation parameters in arid climates

This research discusses some of the issues encountered while developing a set of WGEN parameters for Chile and advice for others interested in developing WGEN parameters for arid climates. The WGEN program is a commonly used and a valuable research tool; however, it has specific limitations in arid climates that need careful consideration. These limitations are analysed in the context of generating a set of WGEN parameters for Chile. Fourteen to 26 years of precipitation data are used to calculate precipitation parameters for 18 locations in Chile, and 3–8 years of temperature and solar radiation data are analysed to generate parameters for seven of these locations. Results indicate that weather generation parameters in arid regions are sensitive to erroneous or missing precipitation data. Research shows that the WGEN-estimated gamma distribution shape parameter ( α) for daily precipitation in arid zones will tend to cluster around discrete values of 0 or 1, masking the high sensitivity of these parameters to additional data. Rather than focus on the length in years when assessing the adequacy of a data record for estimation of precipitation parameters, researchers should focus on the number of wet days in dry months in a data set. Analysis of the WGEN routines for the estimation of temperature and solar radiation parameters indicates that errors can occur when individual ‘months’ have fewer than two wet days in the data set. Recommendations are provided to improve methods for estimation of WGEN parameters in arid climates.

제빙화학제 살포로 인한 콘크리트 교량 바닥판의 철근부식 시작시기의 예측

초록·키워드 목차 오류제보하기 등록된 정보가 없습니다. ABSTRACT1. 서론2. 연구개요 및 방법3. 연구 결과 및 분석4. 결론참고문헌요약

An investigation of cold cloud formation with a three‐dimensional model with explicit microphysics

In the framework of the European Union‐funded project “Investigation of Cloud by Ground‐based and Airborne Radar and Lidar” (CARL) the Regional Atmospheric Modeling System (RAMS) was used in order to study ice crystal formation and evolution in a cold cloud formation during a field program over Palaiseau, France. Sensitivity tests were performed so as to bind the uncertainty from various factors controlling model results. Emphasis is given to the sensitivity of the model with respect to the shape parameter of gamma distribution in the cloud microphysics module. Sensitivity analysis of the model was also performed in relation to the initialization of the simulation. The results are compared to in situ and remote sensing observations of the cloud formation. The analysis revealed that the model was able to reproduce the cloud characteristics (e.g., the spatial and temporal variability of the phenomena and the cloud geometry) in a satisfactory way. A detailed comparison of the model results with aircraft data showed that the model‐calculated water content and number concentration deviate significantly for the small‐size particle bin (2–47 microns) but are in good agreement for the medium‐ (25–800 microns) and large‐size (200–6400 microns) bins. The differences for the smaller particles can partially be attributed to both poor performance of the microphysical algorithms and instrument inaccuracies. Some differences for the larger particles can be attributed either to the definition of the cloud boundaries by the model or to disturbances caused by the ascent path of the aircraft or both. The time of model initialization is also an important factor affecting cloud formation during the first few hours of the simulation. The performed simulations and model/data intercomparisons showed that RAMS is able to reproduce most of the microphysical parameters of cold cloud formations satisfactorily while utilizing conventional meteorological fields and observations for initial and boundary conditions.

Robustness of Sum of Squared Ranks Test

Limiting Pitman efficiencies of the sum of squared ranks test relative to best tests for scale alternative detection are obtained for some specific continuous asymmetrical distributions which have mass confined to the positive axis. In particular the A.R.E. of this test to best tests for gamma distributions is maximized (.9372) when the gamma distribution shape parameter is between five and six. Also this test is an asymptotic locally most powerful rank test for detecting scale alternatives with respect to the distribution formed by doubling the density function of the t distribution with two degrees of freedom over its positive domain.