General Distribution Research Articles

Fitting the Distribution of Linear Combinations of t − Variables with more than 2 Degrees of Freedom

The linear combination of Student’s t random variables (RVs) appears in many statistical applications. Unfortunately, the Student’s t distribution is not closed under convolution, thus, deriving an exact and general distribution for the linear combination of K Student’s t RVs is infeasible, which motivates a fitting/approximation approach. Here, we focus on the scenario where the only constraint is that the number of degrees of freedom of each t − RV is greater than two. Notice that since the odd moments/cumulants of the Student’s t distribution are zero and the even moments/cumulants do not exist when their order is greater than the number of degrees of freedom, it becomes impossible to use conventional approaches based on moments/cumulants of order one or higher than two. To circumvent this issue, herein we propose fitting such a distribution to that of a scaled Student’s t RV by exploiting the second moment together with either the first absolute moment or the characteristic function (CF). For the fitting based on the absolute moment, we depart from the case of the linear combination of K = 2 Student’s t RVs and then generalize to K ≥ 2 through a simple iterative procedure. Meanwhile, the CF-based fitting is direct, but its accuracy (measured in terms of the Bhattacharyya distance metric) depends on the CF parameter configuration, for which we propose a simple but accurate approach. We numerically show that the CF-based fitting usually outperforms the absolute moment-based fitting and that both the scale and number of degrees of freedom of the fitting distribution increase almost linearly with K .

New national and regional plant records: Contribution to the flora of the Old World countries

This paper presents new data on the occurrence of 16 vascular plant species from five Eurasian countries obtained during field explorations, as well as during taxonomic revisions of herbarium materials. Five taxa (<i>Draba fladnizensis</i>, <i>Gentiana orbicularis</i>, <i>Helianthus giganteus</i>, <i>Symphyotrichum cordifolium</i>, <i>Thalictrum alpinum</i>) are recorded for the first time from Poland, five (<i>Achnatherum jacquemontii</i>, <i>Arrhenatherum elatius</i>, <i>Dittrichia graveolens</i>, <i>Geranium pyrenaicum</i>, <i>Stipa</i> × <i>balkanabatica</i>) from Tajikistan, three (<i>Achnatherum sibiricum</i>, <i>Asyneuma thomsonii</i>, <i>Stipa</i> × <i>balkanabatica</i>) from Kyrgyzstan, one (<i>Orobanche bartlingii</i>) from Turkey, one (C<i>alamagrostis obtusata</i>) from China and one (<i>Calamagrostis emodensis</i>) from the Gansu Province in China. In addition, <i>Hieracium piliferum</i>, considered extinct in Poland, was rediscovered. For each species, synonyms, taxonomy with remarks on recognition and differentiation of the species from the most similar taxa occurring in a given area, general distribution, habitat preferences, as well as a list of recorded localities (often far from the previously known areas) are presented. As a result of the morphological comparison of specimens representing <i>Stipa</i> × <i>balkanabatica</i> collected in Tajikistan and Kyrgyzstan with the type specimen collected from Turkmenistan, we decided to describe a new variety named <i>S</i>. × <i>balkanabatica</i> var. <i>alaiensis</i> M. Nobis & Klichowska, <i>var. nov</i>. Additionally, based on the analysis of phytosociological relevés prepared during field studies in the western Pamir Alai Mts (in Kyrgyzstan and Tajikistan), a new association of chasmophytic plants named <i>Asperulo oppositifoliae</i>–<i>Achnatheretum jacquemontii</i> M. Nobis, Klichowska & A. Nowak, is also described.

Karyo-geographical analysis of Armenian flora

Approximately 3,800 species of vascular plants have been registered in the flora of Armenia, of which 789 chromosome numbers are known. Additionally, many species have several cytoraces in Armenia (a total of 898 cytoraces were recorded). These species were analysed from a phytogeographical point of view. Their distribution by floristic regions of the republic, altitudinal zones, and vegetation type has been revealed. Geographical elements were established based on general distribution. As a result of the analysis, it was found that Armenian flora was formed over a long period, starting from the Tertiary period, and is composed of nearly equal proportions of migrants from the Boreal and Ancient Mediterranean sub-kingdoms, and species formed on the Armenian Highlands and on the Greater Caucasus. A significant percentage of endemics (mainly neoendemics) indicate that the territory of Armenia is also an arena of intensive formation and speciation. At the same time, a large karyological diversity among species whose distribution is confined to the Ancient Mediterranean or its several parts, including the Armeno-Iranian province, indicates that speciation took place in these territories. The “northern root” species, Boreal and Caucasian, came to Armenia mainly in the form of karyologically stable cytoraces.

A multiple scattering formulation to design meta-trenches for mitigating low-frequency ground-borne vibrations induced by surface railways and subways

We propose a multiple scattering formulation to investigate the performance of meta-trenches. The meta-trench is a novel device, composed of an array of resonant units buried in the ground in a proper arrangement, aimed at reducing the railway and/or subway induced ground motion by exploiting its scattering and resonant properties. Compared to classical open trenches, the resonators contribute to improving the wave mitigation performance of the trench in the low-frequency regime.The proposed formulation allows to consider the wave source anywhere in the half-space and a generic distribution of resonators in terms of number and position. The incident wave field generated by the source, such as a train or subway, along with the scattered wave fields produced by the resonant units that constitute the meta-trench, are modeled via Green’s functions. The multiple scattering formulation enables the solution of coupled wave problems by determining the amplitudes of scattered wave fields at various frequencies. Through comparison with finite element simulations, we demonstrate that in both buried source (i.e., subway) and surface-located source (i.e., ground railway) scenarios, our analytical formulation is able to properly model the dynamics of the coupled problems with a noticeable computational cost saving. Opening to fast and reliable parametric simulations, our formulation allows for a deeper knowledge of the wave interaction processes, resulting thus in a reliable tool for predicting the coupled wave field under both bulk and Rayleigh waves.

DESAIN PENGEMBANGAN JARINGAN TRANSPORTASI PENYEBERANGAN UNTUK MENDUKUNG DISTRIBUSI GENERAL CARGO ANTAR-PULAU DI PROVINSI MALUKU

Ferry transport plays an important role in the general cargo distribution process in the Maluku region. However, the network pattern that has been applied has not been effective so that the area in the southern part is still isolated because the frequency of ship stops is more than two weeks. This condition impedes the distribution of general cargo, increases logistics costs and reduces industrial competitiveness. The purpose of this research is to evaluate and develop an optimal crossing transport network through simulating the distance and shipping time. The results showed that the existing pattern requires 109.05 hours of travel time to reach 2,103 km as the farthest distance. The scenario for developing the multiport calling pattern requires 1 ship to sail the primary route, covering the farthest distance of 3,442 km in 178.27 hours. Scenario I hub and spoke pattern requires 2 ships to sail the primary route, covering the farthest distance of 1,872 km in 96.96 hours. Scenarios II and III require 3 ships to sail the primary route, covering the farthest distance of 2,336 km in 120.99 hours. These results confirm that the hub and spoke pattern is more optimal than the multiport calling pattern even though it requires more ship units. Thus, the hub and spoke scenario III pattern is more appropriate to be applied as an inter island crossing transport network pattern in the Maluku region because it is able to reach all areas so that it can support the distribution of general cargo.

Bayesian geostatistical modeling for discrete‐valued processes

AbstractWe introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on nearest‐neighbor mixture processes (NNMP), referred to as discrete NNMP. To define the joint probability mass function (pmf) over a set of spatial locations, we build from local mixtures of conditional pmfs using a directed graphical model, with a directed acyclic graph that summarizes the nearest neighbor structure. The approach supports direct, flexible modeling for multivariate dependence through specification of general bivariate discrete distributions that define the conditional pmfs. In particular, we develop a modeling and inferential framework for copula‐based NNMPs that can attain flexible dependence structures, motivating the use of bivariate copula families for spatial processes. Moreover, the framework allows for construction of models given a pre‐specified family of marginal distributions that can vary in space, facilitating covariate inclusion. Compared to the traditional class of spatial generalized linear mixed models, where spatial dependence is introduced through a transformation of response means, our process‐based modeling approach provides both computational and inferential advantages. We illustrate the methodology with synthetic data examples and an analysis of North American Breeding Bird Survey data.

A general unit hydrograph distribution and its application on the marginal distribution of global wind speed

We here introduce a simple, general, and analytical method based on the general unit hydrograph (GUH) theory proposed by Guo (2022a, 2022b, 2022c) to describe wind speed marginal distribution. Wind speed probability is generally described by the Weibull distribution; however, its accuracy depends on the contribution made by null wind speed (owing to its zero initial condition). To overcome this disadvantage, we propose a three-parameter GUH distribution with significant flexibility in modeling symmetric heavy-tailed distributions as well as skewed distributions. We show that our proposed GUH distribution corresponds to a generalized logistic distribution that contains both type I and type II generalized logistic distributions. The shape properties of the GUH distribution are discussed along with a simple method for estimating parameters by means of least squares methods. The flexibility of the proposed GUH distribution was assessed by applying it to a well reconstructed global gridded wind speed dataset. Subsequently, we quantify the changes caused by a reversal in global surface wind speed stilling using our GUH distribution. Finally, we confirm that our proposed GUH model agrees with reconstructed wind speed data better than conventional Weibull distribution models, which suggests that the new distribution can be a useful tool for sustainable development of wind energy.

Flow dynamics and noise generation mechanisms in supersonic underexpanded rectangular and planar jets

In this study, large eddy simulations of two rectangular jets with different aspect ratios and one planar jet with spanwise periodic boundaries are carried out in an attempt to investigate and clarify some key issues regarding the flow dynamics and noise generation mechanisms for the screech tone. The substantial effects of the nozzle configuration on shock structures and noise are first revealed in detail. It is found that when the lateral confinement is weakened, the spacing of the shock cells increases and the jet oscillates more intensively in the minor-axis plane, increasing the noise level and altering the screeching frequency. By analyzing the pressure fluctuations of the shear layer in the wavenumber-frequency space, different kinds of waves in these supersonic jets are examined. Importantly, it is revealed that the guided jet wave should play a dominant role in closing the resonance loops rather than the acoustic wave. Moreover, the energy-containing structures with pertinent frequencies are extracted by employing the reduced-order variational mode decomposition, and some underlying flow dynamics are presented. Especially, a novel mechanism has been identified: the low-frequency stretching motions of shock cells have a significant modulation effect on the screeching amplitude in the planar jet. Furthermore, with the aid of the multi-process acoustic theory, the characteristics of physical noise sources are diagnosed, particularly the source mechanisms related to the screech tone. The general structures and distribution of the kinematic noise source Sβ and entropy noise source Se are presented. Sβ mainly exhibits a vortex-like structure near the nozzle, while Se exhibits a lamellar bilayer structure. The spatiotemporal correlations between the physical sources and far-field noise show that the dominant mechanisms for the screech tone rely on the nozzle configuration and the screech tone tends to be produced by multiple sources in all cases.

Event-Based Distributed Secondary Control for AC Islanded Microgrid With Semi-Markov Switched Topology Under Cyber-Attacks

The operation of a microgrid (MG) is easily affected by the environment, which leads to the change of communication topology among distributed generations (DGs). Most of the existing results on secondary control of MG consider that the topology connection is fixed, or just simply switched by arbitrary form. In this article, a more general semi-Markov process is introduced to describe such switching, i.e., the switching of communication topology is regarded as a random change process of system mode under general probability distribution. Then, out of the comprehensive consideration of inevitable network constraints, this article proposes distributed resilient secondary control method for AC islanded MG. In our control strategy, the network security, communication burden, and transmission delay are all considered in the controller design. An event detection mechanism is used as the transmission protocol for information interaction among DGs, reducing the communication burden effectively. And a cyber-attack model is introduced to follow the Bernoulli distribution, and the neighbors' information of each DG may be attacked with possible probability. Based on feedback linearization, the studied secondary control problem is cast into distributed tracking synchronization of first-order multiagent systems. The Lyapunov functional method is used to prove the proposed strategy theoretically, and its effectiveness is verified by a modified IEEE 34 bus test system. The result shows that the proposed method can reduce the communication numbers by over 80% under the premise of realizing frequency restoration and accurate real power sharing of AC islanded MG, and the transmission rate is also reduced by about 40% compared with the existing general method.

On Absoluteness and Stationary Condition of WMDS for Range-Based Localization

Weighted multidimensional scaling (WMDS), an algorithm extending multidimensional scaling (MDS), has been utilized in a broad spectrum of localization. However, there are still two unsolved theoretical questions. (i) The estimator provided by MDS depicts a relative placement of targets which requires further Procrustes analysis to recover the actual placement, referred to as the absolute placement. This fact produces a question: Does the estimator of WMDS is still relative? If not, what underlying mechanisms assert the absoluteness? (ii) It has been proved that WMDS attains the Cramér-Rao lower bound (CRLB) when the ranging distribution is Gaussian. Does it hold for a general distribution? If not, what restrictions on distributions are required? Motivated by such theoretical incompleteness, this paper offers an in-depth theoretical analysis on WMDS in the scheme of range-based localization. With regard to question (i), we reveal the mechanisms that assert the estimator of WMDS always represents exactly the actual locations, and prove that the absoluteness is introduced at the moment of variable separation and all the subsequent matrix equation transformations preserve the absoluteness. As for question (ii), the functional behaviors and maximum condition of CRLB are examined under a general ranging distribution. Then, via the comparison to the variance of WMDS estimator, the stationary condition on ranging distributions for WMDS to attain the CRLB is provided. Extensive simulations are performed to validate the theoretical conclusions numerically. And there exists conformity between numerical and theoretical results.

MODELING AND FORECASTING OF THE VOLATILITY OF ALL-SHARE INDEX OF NIGERIAN STOCK EXCHANGE MARKET

This paper modeled and forecasted the volatility of the Nigerian Stock Exchange Market while incorporating trade volume from January 2022 to December 2024 using both symmetric and asymmetric volatility models such as ARCH, GARCH, GARCH-M, EGARCH, TGARCH, and PGARCH each in Normal, Students-t and Generalized Error Distributions. The results revealed the following facts: the volatility of the market returns could best be modeled using PGARCH (1, 3) model in normal error distribution, there is evidence of positive leverage effect which reflects that positive shocks induce a larger increase in volatility when compared to the negative shocks of equal magnitude, news about volatility from the previous periods has an explanatory power on current volatility, there is volatility clustering in the market returns, changes in the market returns are explosive, the market risk and returns are inversely related, and the out-sample forecast of the market volatility for the next 2years shows that there will be a low volatility from March to September of the year 2023 and then an increase in volatility up to December 2024. However, for policy and investment decision the paper recommends taking the news on volatility into consideration while forming expectations in the market, investors could invest more within March to September 2023 as the market risk and returns are inversely related, following the forecast estimate that the volatility will be on increase from October 2023 up to December 2024 within which investors are likely to invest less as the market risk and returns are inversely related monetary authority could contract the money supply so as to control the problem of idle cash if the percentage of the investors in the risk-averse category is greater than that of risk-lovers and risk diversifiers categories.

Stronger Challengers can Cause More (or Less) Conflict and Institutional Reform

Prominent theories propose that commitment problems drive phenomena such as war and democratization. However, existing work disagrees about a basic question: how does a challenger’s coercive strength affect prospects for conflict and/or institutional reform? We establish that the relationship depends on how challenger strength affects the average and maximum probability of winning a conflict in a given period (“threat”). We analyze a formal model with a general distribution of threats, and conceptualize challenger strength as affecting this distribution. If the maximum threat is fixed and stronger challengers pose a higher average threat, then weak challengers will rebel (absent reform) during the rare periods they pose a high threat. However, if stronger challengers pose a greater maximum threat, then they are harder to buy off. Applying these insights advances theoretical and empirical debates about democratization.

Analysing far-red SIF directional anisotropy of three structurally contrasting forest canopies towards improved GPP estimation

Solar-induced chlorophyll fluorescence (SIF) is used to estimate terrestrial gross primary production (GPP) due to its physiological link to photosynthesis. However, strong angular variations in satellite-observed SIF (SIFobs), especially for forest canopies with a high structural heterogeneity, hampers robust estimation of GPP. Here, we use directional SIFobs datasets from OCO-2 and TROPOMI satellite sensors and the 3D discrete anisotropic radiative transfer model to investigate the directional properties of far-red SIFobs and their relationships with two GPP products obtained from MODIS and FluxCom datasets for three European forest types with contrasting canopy structures, i.e., boreal, temperate and Mediterranean forests. We found bowl-like angular distribution patterns of SIFobs in both observed and simulated boreal and temperate forests, but no generic distribution pattern of SIFobs was found for the Mediterranean forest. In our GPP estimation of boreal forest, oblique SIFobs performed better than the widely used nadir SIFobs. However, we did not find an optimal view angle suitable for all three forest types. Further, the angular dependencies and forest structure impacts present in SIFobs were found to still propagate into the estimation of total emitted SIF (SIFtotal), which generally regarded as free of these confounding effects. Finally, our results demonstrate that two commonly used variables, i.e., SIFobs with a constant viewing angle and the approximated SIFtotal, both fail to produce a robust relationship with GPP for the Mediterranean forest. These findings highlight the importance of forest canopy structural heterogeneity, including forest floor, on interpretation of directional satellite SIF observations, even when corrected and expressed as a total canopy SIF emission.

A confirmation of a conjecture on Feldman’s two-armed bandit problem

AbstractThe myopic strategy is one of the most important strategies when studying bandit problems. In 2018, Nouiehed and Ross put forward a conjecture about Feldman’s bandit problem (J. Appl. Prob. (2018) 55, 318–324). They proposed that for Bernoulli two-armed bandit problems, the myopic strategy stochastically maximizes the number of wins. In this paper we consider the two-armed bandit problem with more general distributions and utility functions. We confirm this conjecture by proving a stronger result: if the agent playing the bandit has a general utility function, the myopic strategy is still optimal if and only if this utility function satisfies reasonable conditions.

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

Statistical description of galaxy clusters in Finzi model of gravity

We exploit a new theory of gravity proposed by Finzi, which gives stronger interaction at large scales, to study the thermodynamic description of galaxy clusters. We employ a statistical model to deduce various thermodynamics equations of state. In addition, we analyze the behavior of clustering parameter in comparison to its standard (Newtonian) counterpart. The general distribution function and its behavior with varying strength of clustering parameter are also studied. The possibility of phase transition is investigated and it is observed that a phase transition is possible though hierarchically. We also analyze the model by comparing the results with data available through SDSS-III, and obtain the parameters involved.

Methanogen activity and microbial diversity in Gulf of Cádiz mud volcano sediments.

The Gulf of Cádiz is a tectonically active continental margin with over sixty mud volcanoes (MV) documented, some associated with active methane (CH4) seepage. However, the role of prokaryotes in influencing this CH4 release is largely unknown. In two expeditions (MSM1-3 and JC10) seven Gulf of Cádiz MVs (Porto, Bonjardim, Carlos Ribeiro, Captain Arutyunov, Darwin, Meknes, and Mercator) were analyzed for microbial diversity, geochemistry, and methanogenic activity, plus substrate amended slurries also measured potential methanogenesis and anaerobic oxidation of methane (AOM). Prokaryotic populations and activities were variable in these MV sediments reflecting the geochemical heterogeneity within and between them. There were also marked differences between many MV and their reference sites. Overall direct cell numbers below the SMTZ (0.2-0.5 mbsf) were much lower than the general global depth distribution and equivalent to cell numbers from below 100 mbsf. Methanogenesis from methyl compounds, especially methylamine, were much higher than the usually dominant substrates H2/CO2 or acetate. Also, CH4 production occurred in 50% of methylated substrate slurries and only methylotrophic CH4 production occurred at all seven MV sites. These slurries were dominated by Methanococcoides methanogens (resulting in pure cultures), and prokaryotes found in other MV sediments. AOM occurred in some slurries, particularly, those from Captain Arutyunov, Mercator and Carlos Ribeiro MVs. Archaeal diversity at MV sites showed the presence of both methanogens and ANME (Methanosarcinales, Methanococcoides, and ANME-1) related sequences, and bacterial diversity was higher than archaeal diversity, dominated by members of the Atribacterota, Chloroflexota, Pseudomonadota, Planctomycetota, Bacillota, and Ca. "Aminicenantes." Further work is essential to determine the full contribution of Gulf of Cádiz mud volcanoes to the global methane and carbon cycles.

An updated catalogue of the Collembola (Hexapoda) from Colombia and a perspective for unexplored richness.

An updated catalog of Collembola nominal species recorded in Colombia is herein provided, including two new records for the country: Entomobrya linda Soto-Adames, 2002 and Folsomides centralis (Denis, 1931), both found in Reserva Natural Mesenia - Paramillo (Antioquia Department). The data were obtained from the original descriptions, as well as secondary records surveyed until December 2022. I considered localities whose studies contained identification at generic level, but disregarded those who only contained records at family level. For each species, its type locality and general distribution were provided, in addition to the site of record in Colombia, which were plotted on a map. I also present the cumulative number of nominal species recorded and described from Colombia from 1929 to 2022. Colombia has now 38 nominal species (20 endemic) in 21 genera (one endemic, plus 19 without nominal species) and 16 families of Collembola distributed in 22 sites of the 11 departments and five regions. Of this total of families, Bourletiellidae, Collophoridae, Hypogastruridae and Sminthuridae only has generic records, no nominal species. Based on these data, an estimate of the species richness was made suggesting that at the current rate of species records, to recognize 231 to 250 more species (6-7 species every 10 years), it will take about 300 years, and even so this time will not be sufficient to unveil the real fauna of Collembola of the country. For that reason, these results suggest that the Collembola fauna from Colombia is still underestimated in relation to other countries from South America.

Multivariate Lévy-type drift change detection and mortality modeling

In this paper we give a solution to the quickest drift change detection problem for a multivariate Lévy process consisting of both continuous (Gaussian) and jump components in the Bayesian approach. We do it for a general 0-modified continuous prior distribution of the change point as well as for a random post-change drift parameter. Classically, our criterion of optimality is based on a probability of false alarm and an expected delay of the detection, which is then reformulated in terms of a posterior probability of the change point. We find a generator of the posterior probability, which in case of general prior distribution is inhomogeneous in time. The main solving technique uses the optimal stopping theory and is based on solving a certain free-boundary problem. We also construct a Generelized Shiryaev-Roberts statistic, which can be used for applications. The paper is supplemented by two examples, one of which is further used to analyze Polish life tables (after proper calibration) and detect the drift change in the correlated force of mortality of men and women jointly.

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing textbf{G} matrices

Theory predicts that the additive genetic covariance (textbf{G}) matrix determines a population’s short-term (in)ability to respond to directional selection—evolvability in the Hansen–Houle sense—which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.