Parameters Of Gamma Research Articles

Application of the Proposed Technique to Estimate the Bivariate Gamma Model

In this paper, the parameters of the mixed gamma with m components were estimated using model assuming that the variables are not dependent. The method used includes the ideas of the (Wilson-Hilferty (WH) approximation), the (MCLUST) formula, and (the ML principle). The complexities related to parameter estimation and mixture quantitative relation determination area unit reduced thanks to incorporation of a The Wilson-Hilferty approximation (WH) that converts to multivariate Gaussian mixture (MGMM) setup. This methodology was wont to estimate the rate of spleen enlargement in patients with thalassemia (anemia Mediterranean Sea).

Maximum leave-one-out likelihood method for the location parameter of variance gamma distribution with unbounded density

Maximum likelihood estimation of a location parameter fails when the density has unbounded mode. An alternative approach is considered by leaving out a data point to avoid the unbounded density in the full likelihood. This modification gives rise to the leave-one-out (LOO) likelihood. We propose an expectation-conditional maximisation (ECM) algorithm to estimate parameters of variance gamma (VG) distribution with unbounded density by maximising the LOO likelihood. VG distribution has normal mean-variance mixtures representation that facilitates ECM algorithm. K Podgórski, J Wallin [Maximizing leave-one-out likelihood for the location parameter of unbounded densities. Ann Inst Stat Math. 2015;67(1):19–38.] showed that the location parameter estimate which maximises the LOO likelihood is consistent and super-efficient. In the case of repeated data, the LOO likelihood is still unbounded and we extend it to Weighted LOO (WLOO) likelihood. We perform simulations to investigate the accuracy of ECM method using WLOO likelihood and compare it with other likelihood methods, including the alternating ECM with fixed and adaptive caps to the unbounded density, the ghyp package using multi-cycle ECM, and the ECM using LOO likelihood. Lastly, we explore the asymptotic properties of the location parameter estimate of VG distribution such as the optimal convergence rate and asymptotic distribution.

Effects of Re and Co additions on lattice parameters and lattice misfit in cast Ni-based superalloys

Abstract Morphological evolution of gamma prime precipitates was governed by an elemental partitioning ratio between the gamma and gamma prime phases. In the present study, Ni-based MGA 1400 alloy was modified by adding 4 wt% of Re and 6.4 wt% of Co by vacuum arc melting. The effects of Re and Co additions on lattice parameters of gamma and gamma prime phases were studied by TEM and XRD techniques. Calculated lattice misfit values obtained from XRD and TEM techniques were used to identify the shape and morphology of gamma prime precipitated particles after long-term exposure at 1173 K for 1800 ks? After long-term exposure, gamma prime particles became much coarser. The addition of Re retarded the coarsening rate of the gamma prime precipitates, resulting in smaller gamma prime particles at the same annealing times. Even though, both Re and Co atoms are strongly partitioned in the gamma matrix, the effect of Re and Co additions on lattice misfits was contradictory. The addition of Re produced rounded corner cuboidal morphology of gamma prime precipitates due to higher magnitude with negative lattice misfit (−0.3857%), while Co addition provided a more rounded shape of gamma prime particles due to the lattice misfit value approach to zero (+0.0936%).

A semiparametric Bayesian method with birth-death Markov Chain Monte Carlo algorithm for extreme mooring tension analysis

A series of 1: 50 model tests have been conducted to study the dynamics of a taut mooring system and two hybrid mooring systems attached to a deep-water semi-submersible in the 100-year wave condition of the South China Sea. Three typical environmental conditions were tested, including head sea, beam sea and quartering sea. The mixture Gamma- Generalized Pareto distribution (GPD) model is applied to study short term extreme dynamic mooring tensions based on the measured data, the results are compared with the estimations from mixture Gamma and two-parameter Weibull models. A birth-death Markov chain Monte Carlo (MCMC) sampling procedure is developed to fit the parameters of a mixture Gamma- GPD via Bayesian inference, and an extensive discussion of the de-clustering procedure, parameters of the prior distribution for threshold and MCMC iteration steps on Bayesian inference are carried out. It is found that the Weibull model underestimates the most probable largest dynamic mooring tensions. On the contrary, the mixture Gamma model overestimates the extreme dynamic mooring tension significantly. The mixture Gamma- GPD can present good estimations of extreme dynamic mooring tension, and its performance is robust to the sample definition, MCMC iteration steps and parameters of threshold prior distribution.

Evaluation of fractures using conventional and FMI logs, and 3D seismic interpretation in continental tight sandstone reservoir

Abstract Due to the complex pore structures and strong heterogeneity of fractured reservoirs, it is a hot and difficult point in petroleum geology to identify fractures using logging principles. In this paper, taking the tight sandstone reservoir of the Chang 8 Member in the Huanjiang Oilfield as an example, field outcrops, cores, thin sections, and logging identification methods were used for quantitative description and fine logging evaluation of fractures. The research shows that high-angle, medium-low-angle, near-vertical, and horizontal fractures are developed in the Chang 8 Member of the Huanjiang Oilfield. The main ones are high-angle fractures, followed by horizontal fractures with a low degree of fillings. Under the constraints of core and imaging logging data, three fracture sensitivity logging parameters of acoustic wave time difference, natural gamma, and dual induction-octalateral resistivity were optimized, and a comprehensive fracture probability index was proposed. Seventy-nine fracture development intervals were identified based on log curve characteristics and fracture probability indexes. The coincidence rate of fracture logging identification results with the core observation and imaging logging interpretation is 80.6%. The research results can provide a theoretical basis for the efficient development of fractured continental tight sandstone reservoirs in similar areas.

Evaluation of gamma and neutron shielding capacities of tellurite glass system with Phy-X simulation software

Newly developed glass system H 3 BO 3 –K 2 CO 3 –MgO–TeO 2 –ZnO–AgNO 3 (HKMTZA) was synthesized by high temperature melting method for gamma and neutron shielding. The parameters of gamma and neutron attenuation are computerized utilizing Phy-X/PSD and for photon energies ranging between 15 KeV and 15 MeV. The newly developed tool is used to calculate the shielding parameters such as mass attenuation coefficient ( μ/ρ ), relative parameters effective atomic number ( Z eff ), half-value layer ( HVL ), tenth value layer ( TVL ), mean free path ( MFP ), and fast neutrons ( Σ R ). Meanwhile, Σ R is enabled to assess the capabilities of the neutron shielding. Because of Ag element which has high atom number, HKMTZA6 has highest Z eff and lowest HVL , TVL . The results of this research revealed that Σ R of this HKMTZA glass system increases with the improving of AgNO 3 and the studied glass system possess higher Σ R value, contrasting with T70V27Z3 glass. And it is closed to the leaded brass alloy (LB), and TeO 2 –B 2 O 3 (TB), illustrating that the HKMTZA glass system possesses excellent properties of neutron shielding. • Glass system with gamma and neutron attenuation properties has been fabricated. • A series of relative radiation parameters are derived by Phy-X/PSD. • Value of neutron shielding factor Σ R are carried out in the range of 0.123–0.100 cm −1 . • THZMKA system is a superior shielding material contrast reported glass and concrete.

Synthesis, gamma and neutron attenuation capacities of boron-tellurite glass system utilizing Phy-X/PSD database

Phy-X/PSD was applied to evaluate the properties of gamma and neutron attenuation of TeO2–B2O3–RnO (R = Mg, K, and Zn) glass systems which is fabricated successfully by high temperature melting method. The abilities of gamma ray shielding were investigated by the relative parameters effective atomic number (Zeff), half-value layer (HVL), tenth value layer (TVL), mean free path (MFP), and fast neutrons (ΣR) which are crucial gamma shielding parameters. Meanwhile, the parameter of ΣR plays an essential role for evaluating the abilities of the neutron shielding. The study results revealed a phenomenon that the improving of TeO2 fraction from 11 mol% to 61 mol% decreases the parameters of gamma shielding μ, μ/ρ, Zeff, and ΣR, and also increases HVL, TVL, and MFP parameters, which based on the high atomic number of tellurium. Furthermore, the prepared glasses were effective shielding material which can reduce fast neutrons as well as gamma rays, illustrating that prepared glass system possesses excellent properties of gamma shielding.

Support Vector Regression Modelling of an Aerobic Granular Sludge in Sequential Batch Reactor.

Support vector regression (SVR) models have been designed to predict the concentration of chemical oxygen demand in sequential batch reactors under high temperatures. The complex internal interaction between the sludge characteristics and their influent were used to develop the models. The prediction becomes harder when dealing with a limited dataset due to the limitation of the experimental works. A radial basis function algorithm with selected kernel parameters of cost and gamma was used to developed SVR models. The kernel parameters were selected by using a grid search method and were further optimized by using particle swarm optimization and genetic algorithm. The SVR models were then compared with an artificial neural network. The prediction results R2 were within >90% for all predicted concentration of COD. The results showed the potential of SVR for simulating the complex aerobic granulation process and providing an excellent tool to help predict the behaviour in aerobic granular reactors of wastewater treatment.

Breast Tissue Characterization Based on Generalised Extreme Value Distribution of Ultrasound Radio-Frequency Data

In this study, an ultrasound Radio-Frequency (RF) data of healthy and tumour breast regions are considered for tissue characterisation. The main aim of this study is to differentiate the consistent statistical distribution of backscattered RF data with the objective of performing semi-automatic segmentation based on statistics. The differentiation considers Gamma, Generalised Extreme Value (GEV), Log-normal, and Rayleigh distributions. The accuracy of the statistical parameters is measured based on the criteria of both the Kolmogorov-Smirnov Test (KS) and Mean Square Error (MSE) goodness of fit. Results show that there is a possibility of using the parameters of Rayleigh, Gamma, and GEV for different healthy and tumour tissue regions, where GEV yields the best goodness of fit test and its parameters have a good potential to be exploited for further study for segmentation purposes.

The effect of using Nano iron oxide in radiological shielding

In this study, some attenuation parameters of gamma shields were studied. This shields consisting of composite materials of Unsaturated polyester as a base material and Nano iron oxide (Fe2O3) and, micro iron (Fe) as reinforcement materials at different percentages (1, 3,5,7and 9)wt%, and with different thickness (1, 1.5, 2, 2.5, 3, 3.5and 4) cm. The results showed that the use of nanoparticles is better than the microparticales in the field of radiation shielding. It has been shown that the values of attenuation parameters of gamma it bitter in the case of nanoparticles than case of the use of micro material.

Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R∞-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain.

An application of Particle Swarm Optimization (PSO) algorithm with daily precipitation data in Campina Grande, Paraíba, Brazil

We study the daily precipitation in the municipality of Campina Grande, estimating the parameters of Gamma, Log-Normal, and Weibull distributions. To evaluate the parameter estimators, we compared the Particle Swarm Optimization (PSO) versus Maximum Likelihood Estimation (MLE) to analyze and understand the behaviour of the daily precipitation in Campina Grande. In most cases, our results show evidence that the PSO algorithm is an efficient and robust technique. Notwithstanding, the algorithm also presents an efficient parameter estimation due to its fast convergence.

Monthly rainfall distributions in Pematangsiantar

Monthly rainfall data for three rainfall stations, Marihat, Bangun and Bah Jambi in Pematangsiantar are investigated during 2007 to 2016 to choose the most appropriate probability distribution in every station. Rainfall data obtained from the Meteorology Climatology and Geophysics Council (BMKG). In this paper Maximum Likelihood Method is used for estimation parameters of distributions Normal, Log Normal and Gamma. After the data is estimated then data is tested using Kolmogorov-Smirnov test. Based on the Kolmogorov-Smirnov test, Normal distribution has been discovered as the most appropriate distribution to represent monthly rainfall in Pematangsiantar.

The Dependence of Sea SAR Image Distribution Parameters on Surface Wave Characteristics

Modeling the statistical distribution of synthetic aperture radar (SAR) images is essential for sea target detection, which is an important aspect of marine SAR applications. The main goal of this study is to determine the effects of sea states and surface wave texture characteristics on the statistical distributions of sea SAR images. A statistical analysis of the Envisat Advanced Synthetic Aperture Radar (ASAR) wave mode images (imagettes), covering a variety of sea states and wave conditions, was carried out to investigate the suitability of the statistical distributions often used in the literature for sea states parameters. The results revealed the variation in the distribution parameters in terms of their azimuthal cutoff wavelength (ACW) and the peak-to-background ratio (PBR) of the SAR image intensity spectra. The shape parameters of Gamma and Weibull distribution are sensitive and monotonously decreasing with respect to PBR, while the scale parameter is sensitive to ACW. The K distribution was shown to perform well, with both high and stable accuracy. The results of this paper provide a parameterized scheme for sea state classifications and can potentially be used for choosing the most suitable distribution model according to sea state when performing sea target detection.

Estimating freeway travel time and its reliability using radar sensor data

ABSTRACTTravel time and its reliability are intuitive system performance measures for freeway traffic operations. This paper proposes a method to estimate travel times based on data collected from roadside radar sensors, considering spatially correlated traffic conditions. Link-level and corridor-level travel time distributions are estimated using these travel time estimates and compared with the ones estimated based on probe vehicle data. The maximum likelihood estimation is used to estimate the parameters of Weibull, gamma, normal, and lognormal distributions. According to the log-likelihood values, lognormal distribution is the best fit among all the tested distributions. Corridor-level travel time reliability measures are extracted from the travel time distributions. The proposed travel time estimation model can well capture the temporal pattern of travel time and its distribution.

Biological Shielding Design of In Vitro Test Facility Boron Neutron Capture Therapy (BNCT) at Radial Piercing Beam Port of Kartini Research Reactor Using MCNPX

<p>This research aimed to determine material specification of radiation biological shielding design of neutron and gamma output on radial piercing beamport of Kartini Research Reactor using MCNPX code, as safety radiation protection purpose of in vitro / in vivo irradiation test facility. Refference input data using parameters of neutron and gamma as result simmulation researcher before as follows Ф<sub>th</sub> is 5.00 x 10<sup>8 </sup>n.cm<sup>-2</sup>s<sup>-1</sup>, Ф<sub>epi</sub> is 1.23 x 10<sup>8</sup> n.cm<sup>-2</sup>s<sup>-1</sup>, Ф<sub>fast </sub>is 1.35 x 10<sup>9</sup> n.cm<sup>-2</sup>s<sup>-1</sup>, Ḋ<sub>γ</sub> is 2.49 x 10<sup>-3</sup> Sv.s<sup>-1</sup>, Ḋ<sub>n</sub> is 3.63 x 10<sup>-1</sup> Sv.s<sup>-1</sup>. [ Dwi W.]</p>Optimation result of simulation using MCNPX to determine specification material for radiation protection safety are parafin block with thickness 75 cm for neutron shielding and covered by material lead (Pb) with thickness 15 cm for gamma shieding. By this optimation for the both thickness materials, determination for neutron and gamma dose rate are as follow , Ḋ<sub>n</sub> = 1,1 x Sv.s<sup>-1</sup> and with Ḋ<sub>γ </sub>= 1,1 x 10<sup>-09 </sup>Sv.s<sup>-1</sup>. Those radiation dose rate of neutron and gamma parameters are still under requirement of safety dose standard that is 2.78 x 10<sup>-9</sup> Sv.s<sup>-1</sup> as regulation of Regulatory Body BAPETEN. [Perka BAPETEN No. 4 Tahun 2014]. It can be concluded that by the Biological Shielding Design of In Vitro Test Facility Boron Neutron Capture Therapy (BNCT)<em> </em>at Radial Piercing Beam Port of Kartini Research Reactor Using MCNPX can operated safely.

절리의 방향분포가 이차원 DFN 시스템의 수리적 특성에 미치는 영향

본 연구는 절리의 방향분포가 절리성 암반의 수리적 특성에 미치는 영향을 평가하기 위하여 등가파이프 연결구조에 기반을 둔 이차원 DFN(discrete fracture network) 유체유동 해석 프로그램 코드를 개발하고 수치실험을 수행하였다. 수치실험에 사용된 이차원 DFN 시스템은 경계효과를 고려하여 <TEX>$32m{\times}32m$</TEX> 영역의 중앙에서 <TEX>$20m{\times}20m$</TEX> 크기의 DFN 블록이다. 두 절리군을 사용하여 절리의 빈도와 길이분포를 고정하고 절리군 선주향의 평균과 표준편차를 달리하며 추계론적으로 생성한 총 15개의 DFN 블록에 대하여 매 <TEX>$30^{\circ}$</TEX> 간격으로 회전하면서 총 12 방향으로 구현한 총 180개 DFN 블록에서 블록수리전도도가 산정되었다. 또한, 각각의 DFN 블록에서 이론적 블록수리전도도, 주 수리전도도텐서 및 평균블록수리전도도를 추정하여 비교분석한 결과, 절리군의 평균 교차각이 작을수록 절리 방향분포의 변동성이 이차원 DFN 시스템의 등가연속체 취급 가능성 및 블록수리전도 특성에 더욱 영향을 미치는 것으로 평가되었다. A program code was developed to calculate block hydraulic conductivity of the 2-D DFN(discrete fracture network) system based on equivalent pipe network, and implemented to examine the effect of joint orientation distribution on the hydraulic characteristics of fractured rock masses through numerical experiments. A rock block of size <TEX>$32m{\times}32m$</TEX> was used to generate the DFN systems using two joint sets with fixed input parameters of joint frequency and gamma distributed joint size, and various normal distributed joint trend. DFN blocks of size <TEX>$20m{\times}20m$</TEX> were selected from center of the <TEX>$32m{\times}32m$</TEX> blocks to avoid boundary effect. Twelve fluid flow directions were chosen every <TEX>$30^{\circ}$</TEX> starting at <TEX>$0^{\circ}$</TEX>. The directional block conductivity including the theoretical block conductivity, principal conductivity tensor and average block conductivity were estimated for generated 180 2-D DFN blocks. The effect of joint orientation distribution on block hydraulic conductivity and chance for the equivalent continuum behavior of the 2-D DFN system were found to increase with the decrease of mean intersection angle of the two joint sets. The effect of variability of joint orientation on block hydraulic conductivity could not be ignored for the DFN having low intersection angle between two joint sets.

Monotonicity in the sample size of the length of classical confidence intervals

It is proved that the average length of standard confidence intervals for parameters of Gamma and normal distributions monotonically decreases with the sample size. The proofs are based on fine properties of the classical Gamma function.

A statistical application of the quantile mechanics approach: MTM estimators for the parameters of t and gamma distributions

In this paper, we revisit the quantile mechanics approach, which was introduced by Steinbrecher and Shaw (Steinbrecher, G. &amp; Shaw, W. T. (2008) Quantile mechanics. European. J. Appl. Math.19, 87–112). Our objectives are (i) to derive the method of trimmed moments (MTM) estimators for the parameters of gamma and Student's t distributions, and (ii) to examine their large- and small-sample statistical properties. Since trimmed moments are defined through the quantile function of the distribution, quantile mechanics seems like a natural approach for achieving objective (i). To accomplish the second goal, we rely on the general large sample results for MTMs, which were established by Brazauskas et al. (Brazauskas, V., Jones, B. L. &amp; Zitikis, R. (2009) Robust fitting of claim severity distributions and the method of trimmed moments. J. Stat. Plan. Inference139, 2028–2043), and then use Monte Carlo simulations to investigate small-sample behaviour of the newly derived estimators. We find that, unlike the maximum likelihood method, which usually yields fully efficient but non-robust estimators, the MTM estimators are robust and offer competitive trade-offs between robustness and efficiency. These properties are essential when one employs gamma or Student's t distributions in such outlier-prone areas as insurance and finance.

Some applications of probability generating function based methods to statistical estimation

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure by simulation and we prove the consistency of the estimator.