Framework Of Statistical Model Research Articles

On the attribution of changes in streamflow conditions to climate variability in North Carolina Piedmont, United States

ABSTRACT Changes in streamflow magnitudes have ecological, hydrological, and geomorphological implications. Improved knowledge and understanding of the drivers of changes in streamflow conditions remain critical in water resource management. Spatiotemporal patterns of changes in streamflow conditions for five flow percentiles between two comparative periods: historical period (1944–1980) and recent period (1984‒2022) were determined in 18 watersheds of North Carolina Piedmont. The observed percentage changes in streamflow magnitudes for the five flow percentiles were attributed to change magnitudes in monthly mean precipitation and monthly mean temperature using a statistical modeling framework (i.e. gamma regression model). The results showed reduced streamflow magnitudes for the 10th, 25th, 50th, and 75th percentile flows, respectively, while an increased streamflow magnitude was found for the 90th percentile flow at many of the sites in recent period. The regression models captured the relationships between change magnitudes in streamflow conditions and changes in climate variables across all the sites.

Understanding seasonal cycle of daily extreme temperatures based on generalized additive model for location, scale and shape with smoothing spline

AbstractThe seasonal cycle (SC) of surface air temperature is a substantial element in climatology. Some basic and important topics in climate change studies are based on accurate and reliable estimation of SCs, such as percentile‐based indices of extremes and probability density function (PDF) changes of daily temperatures. For both of them, most studies characterized SCs using averages of multi‐days windows, which is not smooth and accurate enough representing the extreme thresholds and climatological normal of SCs. It is necessary to construct smooth and reasonable SCs for more accurate estimation of temperature changes on extreme thresholds and PDFs. In this study, we propose a flexible method based on generalized additive models for location scale and shape and penalized b‐spline smoothing technique with respective distributions to construct smooth SCs and SC for extreme temperatures (SCETs). The accuracy of the constructed smooth SCETs is good with the estimation biases of percentiles tending to be zero. The constructed smooth SCET also exhibits good stability over time, such that the magnitude changes of temperatures on each calendar day are close to climatic changes of mean temperature when the concerned period shifts. Based on the constructed smooth SCs, climatic changes by seasons and PDFs between two periods, 1961–1990 and 1991–2020, are examined over China. The increase of thresholds for hot extremes in spring during the recent period is prominent, while the increase of thresholds for daytime cold extremes in summer over a part of central to southern China is also notable. The smooth SCs and SCETs based on our flexible statistical modelling framework can characterize daily extreme temperatures reasonably and accurately, and should be expected to have more applications for a better understanding of climate changes related to distributions and seasonal cycles.

High-Resolution Flood Monitoring Based on Advanced Statistical Modeling of Sentinel-1 Multi-Temporal Stacks

High-resolution flood monitoring can be achieved relying on multi-temporal analysis of remote sensing SAR data, through the implementation of semi-automated systems. Exploiting a Bayesian inference framework, conditioned probabilities can be estimated for the presence of floodwater at each image location and each acquisition date. We developed a procedure for efficient monitoring of floodwaters from SAR data cubes, which adopts a statistical modelling framework for SAR backscatter time series over normally unflooded areas based on Gaussian processes (GPs), in order to highlight flood events as outliers, causing abrupt variations in the trends. We found that non-parametric time series modelling improves the performances of Bayesian probabilistic inference with respect to state-of-the-art methodologies using, e.g., parametric fits based on periodic functions, by both reducing false detections and increasing true positives. Our approach also exploits ancillary data derived from a digital elevation model, including slopes, normalized heights above nearest drainage (HAND), and SAR imaging parameters such as shadow and layover conditions. It is here tested over an area that includes the so-called Metaponto Coastal Plain (MCP), in the Basilicata region (southern Italy), which is recurrently subject to floods. We illustrate the ability of our system to detect known (although not ground-truthed) and smaller, undocumented inundation events over large areas, and propose some consideration about its prospective use for contexts affected by similar events, over various land cover scenarios and climatic settings.

Quantifying climatic and socioeconomic drivers of urban malaria in Surat, India: a statistical spatiotemporal modelling study

Cities are becoming increasingly important habitats for mosquito vectors of disease. The pronounced heterogeneity of urban landscapes challenges our understanding of the effects of climate and socioeconomic factors on mosquito-borne disease dynamics at different spatiotemporal scales. Here, we quantify the impact of climatic and socioeconomic factors on urban malaria risk, using an extensive dataset in both space and time for reported Plasmodium falciparum cases in the city of Surat, northwest India. We analysed 10 years of monthly P falciparum cases resolved at three nested spatial resolutions (seven zones, 32 units, and 478 worker units) with a Bayesian hierarchical mixed model that incorporates the effects of population density, poverty, relative humidity, and temperature, in addition to random effects (structured and unstructured). To reduce dimensionality and avoid correlation of covariates, socioeconomic variables from survey data were summarised into main axes of variation using principal component analysis. With model selection, we identified the main drivers of spatiotemporal variation in malaria incidence rates at each of the three spatial resolutions. We also compared observations to model-fitted cases by quantifying the percentage of predictions within five discrete levels of malaria risk. The spatial variation of urban malaria cases was stationary over time, whereby locations with high and low yearly cases remained largely consistent across years. Local socioeconomic variation could be summarised with three principal components accounting for approximately 80% of the variance. The model that incorporated local temperature and relative humidity together with two of these principal components, largely representing population density and poverty, best explained monthly malaria patterns in models formulated at the three different spatial scales. As model resolution increased, the effect size of humidity decreased, whereas those of temperature and the principal component associated with population density increased. Model predictions accurately captured aggregated total monthly cases for the city; in space-time, they more closely matched observations at the intermediate scale, with around 57% of units estimated to fall in the observed category on average across years. The mean absolute error was lower at the intermediate level, showing that this is the best aggregation level to predict the space-time dynamics of malaria incidence rates across the city with the selected model. This statistical modelling framework provides a basis for development of a climate-driven early warning system for urban malaria for the units of Surat, including spatially explicit prediction of malaria risk several weeks to months in advance. Results indicate environmental and socioeconomic covariates for which further measurement at high resolution should lead to model improvement. Advanced warning combined with local surveillance and knowledge of disease hotspots within the city could inform targeted intervention as part of urban malaria elimination efforts. US National Institutes of Health.

The Impact of Government Policy's Effect on Foreign Direct Investment in United Arab of Emirates

The objective of this study is to assess the impact of governmental policy changes in the United Arab Emirates (UAE) on both inward and outward foreign direct investment (FDI) by utilizing a statistical model framework. This research contributes to the existing body of knowledge focused on the influence of public policies targeting FDI and establishes a specific connection between these policies and outward direct investment (ODI). We particularly examine the consequences of major policy adjustments concerning FDI that were implemented by the UAE government over the period from 1950 to 1995. Our analysis indicates that the UAE's participation in various trade agreements notably enhanced both inward and outward foreign direct investment. However, the UAE's initiatives to regulate FDI through specific agencies had minimal significant effects on either FDI or ODI.

Response of streamflow and nutrient loads in a small temperate catchment subject to land use change

The aim of this study was to quantify the effect of land use change (LUC) implemented to meet nutrient load targets for a freshwater lake in New Zealand. We used the Soil and Water Assessment Tool (SWAT) model in combination with a non-parametric statistical test to determine whether afforestation of 15% of a subcatchment area was adequate to meet assigned nutrient load targets. A regional management authority set nutrient load targets of reduction in total nitrogen (TN) by 0.9 t yr−1 and reduction in total phosphorus (TP) by 0.05 t yr−1 to avoid eutrophication in the receiving waters of a freshwater lake. The load reduction was designed to be achieved through 200 ha of LUC from pasture to trees. Analysis of nutrient loads before, during, and following LUC shows that a 15% increase in forest cover decreased the annual flow (7.2%), TP load (33.3%), and TN load (13.1%). As flow and water quality observations were discrete and at irregular intervals, we used a parametric test and the SWAT model as different lines of evidence to demonstrate the effect of afforestation on flow and water quality. Policymakers concerned with decisions about LUC to improve the quality of receiving waters can benefit from applying our findings and using a statistical and numerical modelling framework to evaluate the adequacy of land use change to support improvements in water quality.

Machinery Health Prognostics With Multimodel Fusion Degradation Modeling

Degradation modeling aims to formulate the health state degradation process of machinery. Commonly used degradation models pay more attention to describing the global increasing or decreasing trend without considering the local fluctuation in the degradation process. To deal with the above issue, this paper proposes a multi-model fusion degradation modeling method. The basic idea is to fuse multiple models to describe various degradation trends of machinery involving the global trend as well as the local fluctuation. A generalized statistical degradation modeling framework is constructed, wherein the degradation process is formulated by fusing multiple models with various degradation trends. The failure event is reinterpreted under the condition of state observations fluctuating around the failure threshold. The probability density functions (PDFs) of the time when the state observation exceeds and drops below the failure threshold are derived, respectively. An iterative matching pursuit (IMP) algorithm is developed to select the optimal models adaptively. A numerical illustration and an experimental study are conducted to verify the proposed method. The results demonstrate its superiority in health prognostics compared with two benchmark methods in cases where the degradation process has dominant local fluctuation.

TRANSPORTATION OF CUTTINGS BY DRILLING MUD IN HORIZONTAL WELLS. PART 1. MODELING THE STRUCTURE OF DISPERSED CURRENTS

Link for citation: Kharlamov S.N., Mehran Janghorbani, Zaykovskiy V.V. Transportation of cuttings by drilling mud in horizontal wells. Part 1. Modeling the structure of dispersed currents. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 10, рр. 34-48. In Rus. The relevance of the research is associated with the development of technical solutions for drilling wells with horizontal endings, in which cleaning the annulus from particles of drilled cuttings in hydraulic transport conditions seems technologically and economically efficient compared to other, for example, mechanical methods. The purpose of the article is to develop a computational methodology/approach to a detailed forecast and deep understanding of the physical mechanism of the influence of hydraulic transport on the well cleaning intensity. Moreover, the strategy of such a study is focused on the choice of flow conditions/rheological parameters of the model, in which the obtained detailed theoretical information on the evolution of the dynamic flow structure should be used in the development of design methods and the formulation of recommendations to engineering personnel for emergency warnings. The object of this study is a new class of viscous currents of dispersed media induced by external and internal forces, characteristic of the functioning of special equipment that ensures the movement of drilling mud with complex rheology in the well through an eccentric annular annulus. Results. The given article is the first part of the study devoted to solving complex problems accompanying the hydraulic transfer of rheologically complex mixtures through wells with an extended horizontal section and their cleaning from drilling cuttings. The first part presents the data on reasonable modeling of hydrodynamics of viscous dispersed mixture within the framework of reference to full equations describing laws of mass conservation, impulse for detection of peculiarities, determination of flow regularities in eccentric area of annular annulus, as well as search for ways of intensification of cleaning under conditions of real drilling. It is assumed that the viscous-inertial-gravitational flow of a liquid of the Herschel–Bulkly type with solid particles (sand) is carried out in conditions of laminar-turbulent, straight-flow and twisted (by the method of a movable wall) flow developing in the space. It is noted that the formation of modes with active and conservative action of external and internal forces allows efficient cleaning of the annulus. System of defining equations of mathematical model of hydrodynamics and mass transfer is analyzed for possibility of taking into account changes in nonlinearity of thermophysical properties, resistance to disturbances at boundaries of flow area and phase separation. It is noted that the prediction of molar processes is carried out within the framework of modern statistical models of the RANS method and the Euler–Lagrangian approach to describing the movement of heterogeneous media implemented in the ANSYS CFD software. It was shown that at the real drilling conditions, the mathematical model is successful in determining the spectrum of local and integral parameters of hydrodynamics and mass transfer in a wide range of changes in drilling conditions, which make it possible to understand the effects of particle sedimentation on the lower wall, the dynamics of vortex separation and the transfer of particles to the low-Reynolds region with a suspended state of the mixture structure and the inertial zone of the flow core. It is noted that the intensity of hydraulic transport downstream is significantly influenced by the conditions of phase entry, rheological characteristics of the mud. The calculations established the flow areas with satisfactory agreement of dynamic characteristics of the flow according to the proposed model with available experimental data, for example, shear stress at the wall, radial distributions of the components of the fluid velocity vector along the length of the well at different angles of deviation of its borehole from the vertical. Moreover, the results of this article should be taken into account when describing the data of the second part, as an addition to the study of hydraulic transport according to the proposed technique of real drilling of horizontal wells with optimal rheological properties of the mud.

Public health factors help explain cross country heterogeneity in excess death during the COVID19 pandemic

The COVID-19 pandemic has taken a devastating toll around the world. Since January 2020, the World Health Organization estimates 14.9 million excess deaths have occurred globally. Despite this grim number quantifying the deadly impact, the underlying factors contributing to COVID-19 deaths at the population level remain unclear. Prior studies indicate that demographic factors like proportion of population older than 65 and population health explain the cross-country difference in COVID-19 deaths. However, there has not been a comprehensive analysis including variables describing government policies and COVID-19 vaccination rate. Furthermore, prior studies focus on COVID-19 death rather than excess death to assess the impact of the pandemic. Through a robust statistical modeling framework, we analyze 80 countries and show that actionable public health efforts beyond just the factors intrinsic to each country are important for explaining the cross-country heterogeneity in excess death.

Simple and flexible sign and rank-based methods for testing for differential abundance in microbiome studies.

Microbiome data obtained with amplicon sequencing are considered as compositional data. It has been argued that these data can be analysed after appropriate transformation to log-ratios, but ratios and logarithms cause problems with the many zeroes in typical microbiome experiments. We demonstrate that some well chosen sign and rank transformations also allow for valid inference with compositional data, and we show how logistic regression and probabilistic index models can be used for testing for differential abundance, while inheriting the flexibility of a statistical modelling framework. The results of a simulation study demonstrate that the new methods perform better than most other methods, and that it is comparable with ANCOM-BC. These methods are implemented in an R-package 'signtrans' and can be installed from Github (https://github.com/lucp9827/signtrans).

MIDDLE SCHOOL STUDENTS’ STATISTICAL REASONING ABOUT DISTRIBUTION IN THEIR STATISTICAL MODELING PROCESSES

Statistical reasoning about a population through samples can be achieved by modeling the relationship between population and sample. One way to do this is to model real data situations in a technology-integrated environment. With this view, we aimed to investigate how middle school students formed distributions and examined their statistical modeling processes through the informal reasoning process within the Reasoning with Informal Statistical Models and Modeling (RISM) framework. The case study reported in this paper focuses on how the conjecture and data models students designed throughout three activities evolved and how their inclusion of a fundamentally probabilistic mechanism matured. Findings show the students approached the distribution probabilistically with their inferences during the modeling process and grasped the statistical concepts they would encounter at a more advanced level. Therefore, we claim that students shifted from understanding empirical distributions to understanding theoretical distributions.

Associations between Dengue Incidence, Ecological Factors, and Anthropogenic Factors in Singapore.

Singapore experiences endemic dengue. Vector control remains the primary means to reduce transmission due to the lack of available therapeutics. Resource limitations mean that vector-control tools need to be optimized, which can be achieved by studying risk factors related to disease transmission. We developed a statistical modelling framework which can account for a high-resolution and high-dimensional set of covariates to delineate spatio-temporal characteristics that are associated with dengue transmission from 2014 to 2020 in Singapore. We applied the proposed framework to two distinct datasets, stratified based on the primary type of housing within each spatial unit. Generalized additive models reveal non-linear exposure responses between a large range of ecological and anthropogenic factors as well as dengue incidence rates. At values below their mean, lesser mean total daily rainfall (Incidence rate ratio (IRR): 3.75, 95% CI: 1.00-14.05, Mean: 4.40 mm), decreased mean windspeed (IRR: 3.65, 95% CI: 1.87-7.10, Mean: 4.53 km/h), and lower building heights (IRR: 2.62, 95% CI: 1.44-4.77, Mean: 6.5 m) displayed positive associations, while higher than average annual NO2 concentrations (IRR: 0.35, 95% CI: 0.18-0.66, Mean: 13.8 ppb) were estimated to be negatively associated with dengue incidence rates. Our study provides an understanding of associations between ecological and anthropogenic characteristics with dengue transmission. These findings help us understand high-risk areas of dengue transmission, and allows for land-use planning and formulation of vector control policies.

Informing management of recovering predators and their prey with ecological diffusion models

The reintroduction and recovery of predators can be ecologically beneficial as well as socially and economically controversial. However, the growth and expansion of predator populations, and thus their ecological, social, and economic impacts, are not static but rather they vary in space and time. We propose a spatiotemporal statistical modeling framework based on ecological diffusion to better inform the ecology and management of recovering predators and their prey. We demonstrate its utility by applying it to a recovering sea otter (Enhydra lutris) population in Southeast Alaska, where sea otters were reintroduced in the late 1960s and have exhibited unprecedented population growth. Estimated parameters yield inferences about movement and population ecology, and our approach provides useful derived quantities, such as local abundance and carrying capacity as well as a quantity we term the equilibrium differential. We used our model to examine how density dependence and carrying capacity of sea otters vary spatially across a region. The diffusion modeling approach we present can be generalized for use in other instances of (re)colonization across taxa to inform management and conservation efforts.

Enabling supra-aortic vessels inclusion in statistical shape models of the aorta: a novel non-rigid registration method.

Statistical Shape Models (SSMs) are well-established tools for assessing the variability of 3D geometry and for broadening a limited set of shapes. They are widely used in medical imaging due to their ability to model complex geometries and their high efficiency as generative models. The principal step behind these techniques is a registration phase, which, in the case of complex geometries, can be a critical issue due to the correspondence problem, as it necessitates the development of correspondence mapping between shapes. The thoracic aorta, with its high level of morphological complexity, poses a multi-scale deformation problem due to the presence of several branch vessels with varying diameters. Moreover, branch vessels exhibit significant variability in shape, making the correspondence optimization even more challenging. Consequently, existing studies have focused on developing SSMs based only on the main body of the aorta, excluding the supra-aortic vessels from the analysis. In this work, we present a novel non-rigid registration algorithm based on optimizing a differentiable distance function through a modified gradient descent approach. This strategy enables the inclusion of custom, domain-specific constraints in the objective function, which act as landmarks during the registration phase. The algorithm's registration performance was tested and compared to an alternative Statistical Shape modeling framework, and subsequently used for the development of a comprehensive SSM of the thoracic aorta, including the supra-aortic vessels. The developed SSM was further evaluated against the alternative framework in terms of generalisation, specificity, and compactness to assess its effectiveness.

Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.

Tail Dependence as a Measure of Teleconnected Warm and Cold Extremes of North American Wintertime Temperatures

Abstract Current models for spatial extremes are concerned with the joint upper (or lower) tail of the distribution at two or more locations. Such models cannot account for teleconnection patterns of 2-m surface air temperature (T2m) in North America, where very low temperatures in the contiguous United States may coincide with very high temperatures in Alaska in the wintertime. This dependence between warm and cold extremes motivates the need for a model with opposite-tail dependence in spatial extremes. This work develops a statistical modeling framework that has flexible behavior in all four pairings of high and low extremes at pairs of locations. In particular, we use a mixture of rotations of common Archimedean copulas to capture various combinations of four-corner tail dependence. We study teleconnected T2m extremes using ERA5 of daily average 2-m temperature during the boreal winter. The estimated mixture model quantifies the strength of opposite-tail dependence between warm temperatures in Alaska and cold temperatures in the midlatitudes of North America, as well as the reverse pattern. These dependence patterns are shown to correspond to blocked and zonal patterns of midtropospheric flow. This analysis extends the classical notion of correlation-based teleconnections to considering dependence in higher quantiles.

Systematic study of prescission neutron multiplicity: Revealing the role of entrance channel magicity

The prescission neutron multiplicities (νpre) are studied for a systematic understanding of the influence of entrance-channel shell closure in fusion-fission dynamics. The existing νpre data are analyzed for reactions with a wide variety of target and projectile combinations. For completeness, the measured νpre data for the fusion-fission reactions with the doubly closed shell 16O projectile on the targets having either proton (204,206Pb) or both proton and neutron (208Pb) shell closure is reanalyzed. Although the measured νpre for 224Th disagree with the available data reported by Rossner et al. (1992) [1], our results are found to be more consistent and follow a systematic trend as described in this letter. Theoretical analysis is performed within the standard statistical model framework, where dissipation strength is used as a tunable parameter. It is observed that irrespective of the compound nuclear excitation energy, the entrance channel magicity imparts an intriguing impact on the dissipation strength. A similar entrance channel effect in the evaporation residue cross-section is also demonstrated. In conclusion, the present analysis establishes an entanglement of the exit channel observables with the entrance channel shell closure. It contradicts the hypothesis of complete equilibrium in compound nuclear reactions.

Light (anti)nuclei production in Pb-Pb collisions at sNN=5.02 TeV

The measurement of the production of deuterons, tritons and He3 and their antiparticles in Pb-Pb collisions at sNN=5.02TeV is presented in this article. The measurements are carried out at midrapidity (|y|< 0.5) as a function of collision centrality using the ALICE detector. The pT-integrated yields, the coalescence parameters and the ratios to protons and antiprotons are reported and compared with nucleosynthesis models. The comparison of these results in different collision systems at different center-of-mass collision energies reveals a suppression of nucleus production in small systems. In the Statistical Hadronisation Model framework, this can be explained by a small correlation volume where the baryon number is conserved, as already shown in previous fluctuation analyses. However, a different size of the correlation volume is required to describe the proton yields in the same data sets. The coalescence model can describe this suppression by the fact that the wave functions of the nuclei are large and the fireball size starts to become comparable and even much smaller than the actual nucleus at low multiplicities.Received 10 February 2023Accepted 16 May 2023DOI:https://doi.org/10.1103/PhysRevC.107.064904Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.©2023 CERN, for the ALICE CollaborationPhysics Subject Headings (PhySH)Research AreasParticle & resonance productionParticle correlations & fluctuationsRelativistic heavy-ion collisionsPropertiesA ≤ 5Accelerators & BeamsNuclear Physics

Precision Public Health Opportunity: Heat-Associated Mortality Greater among Pilgrims during Hajj

Precision Public Health Opportunity: Heat-Associated Mortality Greater among Pilgrims during Hajj

Planck formula for the gluon parton distribution in the proton

In this paper, we describe the gluon parton distribution function (PDF) in the proton, deduced by data from the ATLAS and HERA experiments, in the framework of the parton statistical model. The best fit parameters involved in the Planck formula that describes the gluon distribution are consistent with the results obtained from analysis of LHC deep inelastic proton–proton scattering processes. Remarkably, the agreement between the statistical model and the experimental gluon distributions is obtained with the same value of the “temperature” parameter [Formula: see text] found by fitting the valence parton distributions from deep inelastic scattering. This result corroborates the validity of the statistical approach in the gluon sector.