Alternative Distributions Research Articles

Fractional generalized cumulative residual entropy: properties, testing uniformity, and applications to Euro Area daily smoker data

<abstract><p>The fractional generalized cumulative residual entropy, a broader version of the cumulative residual entropy, holds significance in assessing the uncertainty model of random variables and maintains straightforward connections with reliability models and crucial information. This article represents and modifies some novel features of the fractional generalized cumulative residual entropy and discusses the weak convergence. Additionally, the measure is utilized to assess uniformity, involving the derivation of the limit distribution and an approximation of the test statistic's distribution. Furthermore, the concept of stability is addressed. Moreover, the presentation includes the critical points and power analysis against alternative distributions of this test statistic. Furthermore, a simulation study is carried out to compare the power value of the proposed test with that of other tests of uniformity. Moreover, the uniformity test utilizes real data on daily smokers in the countries of the Euro Area. Finally, our model's exponential distribution is applied to our model's empirical form.</p></abstract>

On the asymptotic power of the “energy” test for equality of two distributions

In the paper the asymptotic distribution and the formula for the asymptotic power are found for the "energy" test in the case of alternative distributions differ from zero distribution by the parameter of shift and/or the parameter of scale. This criterion is an alternative for the well-known Mann-Whitney test but allows to compare distributions that differ by the scale parameter. The efficiency of the results obtained is demonstrated by the stochastic simulation for the normal distribution and the Cauchy distribution.

The Framework for Assessing Changes To Sea-level (FACTS) v1.0: a platform for characterizing parametric and structural uncertainty in future global, relative, and extreme sea-level change

Abstract. Future sea-level rise projections are characterized by both quantifiable uncertainty and unquantifiable structural uncertainty. Thorough scientific assessment of sea-level rise projections requires analysis of both dimensions of uncertainty. Probabilistic sea-level rise projections evaluate the quantifiable dimension of uncertainty; comparison of alternative probabilistic methods provides an indication of structural uncertainty. Here we describe the Framework for Assessing Changes To Sea-level (FACTS), a modular platform for characterizing different probability distributions for the drivers of sea-level change and their consequences for global mean, regional, and extreme sea-level change. We demonstrate its application by generating seven alternative probability distributions under multiple emissions scenarios for both future global mean sea-level change and future relative and extreme sea-level change at New York City. These distributions, closely aligned with those presented in the Intergovernmental Panel on Climate Change Sixth Assessment Report, emphasize the role of the Antarctic and Greenland ice sheets as drivers of structural uncertainty in sea-level change projections.

A family of tests for trend change in failure rate function with right censored data

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: 10.1007/s00362-018-01074-8] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: 10.1109/24.9842] is obtained. Finally some examples of real life data are given for illustrative purpose.

Testing Equality of Several Distributions at High Dimensions: A Maximum-Mean-Discrepancy-Based Approach

With the development of modern data collection techniques, researchers often encounter high-dimensional data across various research fields. An important problem is to determine whether several groups of these high-dimensional data originate from the same population. To address this, this paper presents a novel k-sample test for equal distributions for high-dimensional data, utilizing the Maximum Mean Discrepancy (MMD). The test statistic is constructed using a V-statistic-based estimator of the squared MMD derived for several samples. The asymptotic null and alternative distributions of the test statistic are derived. To approximate the null distribution accurately, three simple methods are described. To evaluate the performance of the proposed test, two simulation studies and a real data example are presented, demonstrating the effectiveness and reliability of the test in practical applications.

Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear data

Abstract The probability integral transform of a continuous random variable X X with distribution function F X {F}_{X} is a uniformly distributed random variable U = F X ( X ) U={F}_{X}\left(X) . We define the angular probability integral transform (APIT) as θ U = 2 π U = 2 π F X ( X ) {\theta }_{U}=2\pi U=2\pi {F}_{X}\left(X) , which corresponds to a uniformly distributed angle on the unit circle. For circular (angular) random variables, the sum modulus 2 π \pi of absolutely continuous independent circular uniform random variables is a circular uniform random variable, that is, the circular uniform distribution is closed under summation modulus 2 π \pi , and it is a stable continuous distribution on the unit circle. If we consider the sum (difference) of the APITs of two random variables, X 1 {X}_{1} and X 2 {X}_{2} , and test for the circular uniformity of their sum (difference) modulus 2 π \pi , this is equivalent to test of independence of the original variables. In this study, we used a flexible family of nonnegative trigonometric sums (NNTS) circular distributions, which include the uniform circular distribution as a member of the family, to evaluate the power of the proposed independence test by generating samples from NNTS alternative distributions that could be at a closer proximity with respect to the circular uniform null distribution.

Optimized Virtual Sources Distributions for 3-D Ultrafast Diverging Wave Compounding Imaging: A Simulation Study.

Ultrafast ultrasound imaging allows observing rapid phenomena; combined with 3-D imaging it has the potential to provide more accurate analysis on organs which leads, at the end, to better diagnosis. Coherent compounding using diverging waves is commonly used to reconstruct high quality images on large volumes while keeping frame rate high enough to allow dynamic analysis. In practice, the virtual sources that drive the diverging waves are often distributed by a deterministic way: following a regular grid, concentric rings and spirals. Even though those deterministic distributions can offer various trade-off in terms of imaging performance, other distributions can be considered to improve imaging performance. It is herein suggested to look at alternative virtual sources distributions for optimizing the lateral resolution and the secondary lobes level on several PSFs by means of a multiobjective genetic algorithm. The optimization framework leads to seven pseudo-irregular distributions of virtual source distributions that have not yet been found in the literature. An analysis on the imaging performance with a simulated phantom shows that these new distributions offer different trade-offs between lateral resolution and contrast, respectively measured on point-like reflectors and anechoic cysts. As an example, one of these optimized distributions improves the lateral resolution by 16% and gives equivalent contrast values on cysts, when compared to a concentric-rings-based distribution.

Unveiling abundance-dependent metabolic phenotypes of microbial communities.

Constraint-based modeling has risen as an alternative for characterizing metabolism of communities. Adaptations of flux balance analysis have been proposed to model metabolic interactions, which in most cases consider the maximization of biomass production as their objective. In nature, novel essential functions are not directly related to cell growth force communities to display suboptimal growth rates. These suboptimal states allow a degree of plasticity in their metabolism, thus allowing quick shifts between alternative flux distributions as an initial response to environmental changes. In this work, we introduce the abundance-growth space as a representation of metabolic phenotypes of a community. This space is defined by the composition of a community, represented by its members' relative abundances, and their growth rate. The analysis of this space allows us to pinpoint how critical reactions respond to shifts of the environment, showing where changes in community plasticity occur. Interestingly, it highlights the relevance of the relative abundance of its members in the lost or gain of plasticity. This method is applied to two simple communities that exchange metabolites. A synthetic community of two mutant Escherichia coli strains and an environmental bioleaching community composed by Acidithiobacillus ferrooxidans Wenelen and Sulfobacillus thermosulfidooxidans Cutipay, where only Cutipay consumes organic matter disposed of by the community.IMPORTANCEIn nature, organisms live in communities and not as isolated species, and their interactions provide a source of resilience to environmental disturbances. Despite their importance in ecology, human health, and industry, understanding how organisms interact in different environments remains an open question.In this work, we provide a novel approach that, only using genomic information, studies the metabolic phenotype exhibited by communities, where the exploration of suboptimal growth flux distributions and the composition of a community allows to unveil its capacity to respond to environmental changes, shedding light of the degrees of metabolic plasticity inherent to the community.

A Comparative Assessment of Five Different Distributions Based on Five Different Optimization Methods for Modeling Wind Speed Distribution

Determining wind regime distribution patterns is essential for many reasons; modelling wind power potential is one of the most crucial. In that regard, Weibull, Gamma, and Rayleigh functions are the most widely used distributions for describing wind speed distribution. However, they could not be the best for describing all wind systems. Also, estimation methods play a significant role in deciding which distribution can achieve the best matching. Consequently, alternative distributions and estimation methods are required to be studied. An extensive analysis of five different distributions to describe the wind speeds distribution, namely Rayleigh, Weibull, Inverse Gaussian, Burr Type XII, and Generalized Pareto, are introduced in this study. Further, five metaheuristic optimization methods, Grasshopper Optimization Algorithm, Grey Wolf Optimization, Moth-Flame Optimization, Salp Swarm Algorithm, and Whale Optimization Algorithm, are employed to specify the optimum parameters per distribution. Five error criteria and seven statistical descriptors are utilized to compare the good-of-fitness of the introduced distributions. Therefore, this paper provides different important methods to estimate the wind potential at any site.

Using genetic algorithms to optimize the location of transducers for an active noise barrier

The effectiveness of an active noise barrier is heavily dependent on the positioning of secondary sources and error sensors. Typically, these components are located at the edge of the barrier; however, research suggests that alternative distributions may improve the performance of the active barrier. This paper utilizes a genetic optimizer to determine optimal transducer locations based on specific criteria. Two approaches are employed: the Two-step approach which, first identifies optimal control source positions and then seeks the best error microphone locations, and the Multi-parameter approach, which optimizes all active noise control parameters simultaneously. The acoustic fields of primary and secondary sources are analyzed for various numbers of control sources progressively increasing from 2 to 10 units. Results indicate that the Multi-parameter approach achieves higher outcomes and requires less computational effort. This approach is more desirable than the Two-step approach. The best configuration for the active noise barrier is determined to be control sources and error microphones placed at a height below the barrier’s edge and are distributed with an interval between a half and a full wavelength. The number of error sensors should be close to the number of secondary sources and both transducers should be placed at the farthest distance from the barrier surface, but oppositely. Furthermore, the study shows that when the primary noise source is close to the barrier adjacent transducers should not be spaced uniformly.

On the formation of GW190521-like binary black hole merger systems

ABSTRACT GW190521 is the most massive merging binary black hole (BBH) system detected so far. At least one of the component BHs was measured to lie within the pair-instability supernova (PISN) mass gap (∼50–135 M⊙), making its formation a mystery. However, the transient observed signal allows alternative posterior distributions. There was suggestion that GW190521 could be an intermediate-mass ratio inspiral, with the component masses m1 ∼ 170 M⊙ and m2 ∼ 16 M⊙, happening to straddle the PISN mass gap. Under this framework, we perform binary population synthesis to explore the formation of GW190521-like systems via isolated binary evolution. We numerically calculate the binding energy parameter for massive stars at different metallicities, and employ them in our calculation for common envelope evolution. Our results prefer that the progenitor binaries formed in metal-poor environment with $\rm Z\le 0.0016$. The predicted merger rate density within redshift z = 1.1 is ${\sim} 4\times 10^{-5}{\text {--}}5\times 10^{-2} \, \rm Gpc^{-3}yr^{-1}$. We expect that such events are potentially observable by upcoming both space and ground-based gravitational wave detectors.

Global application of National Comprehensive Cancer Network resource-stratified guidelines for systemic treatment of colon cancer: a population-based, customisable model for cost, demand, and procurement.

Resource-stratified guidelines (RSGs) can inform systemic treatment decisions in the face of limited resources. The objective of this study was to develop a customisable modelling tool to predict the demand, cost, and drug procurement needs of delivering National Comprehensive Cancer Network (NCCN) RSG-based systemic treatment for colon cancer. We developed decision trees for first-course systemic therapy for colon cancer based on the NCCN RSGs. Decision trees were merged with data from the Surveillance, Epidemiology, and End Results programme, the International Agency for Research on Cancer's GLOBOCAN 2020 national estimates for colon cancer incidence, country-level income data, and data on drug costs from Redbook (USA), the Pharmaceutical Benefits Scheme (Australia), and the Management Sciences for Health 2015 International Medical Products price guide to estimate global treatment needs and costs, and forecast drug procurement. Simulations and sensitivity analyses were used to explore the effect of scaling up services globally and the effect of alternative stage distributions on treatment demand and cost. We generated a customisable model, in which estimates can be tailored to local incidence, epidemiological, and costing data. First-course systemic therapy is indicated in 608 314 (53·6%) of 1 135 864 colon cancer diagnoses in 2020. Indications for first-course systemic therapy are projected to rise to 926 653 in 2040; the indications in 2020 might be as high as 826 123 (72·7%), depending on stage distribution assumptions. Adhering to NCCN RSGs, patients with colon cancer in low-income and middle income countries (LMICs) would constitute 329 098 (54·1%) of 608 314 global systemic therapy demands, but only 10% of global expenditure on systemic therapies. The total cost of NCCN RSG-based first-course systemic therapy for colon cancer in 2020 would be between about US$4·2 and about $4·6 billion, depending on stage distribution. If all patients with colon cancer in 2020 were treated according to maximal resources, global expenditure on systemic therapy for colon cancer would rise to around $8·3 billion. We have developed a customisable model that can be applied at global, national, and subnational levels to estimate systemic treatment needs, forecast drug procurement, and calculate expected drug costs on the basis of local data. This tool can be used to plan resource allocation for colon cancer globally. None.

Fitting Cumulus Cloud Size Distributions From Idealized Cloud Resolving Model Simulations

AbstractWhereas it is now widely accepted that cumulus cloud sizes are power‐law distributed, characteristic exponents reported in the literature vary greatly, generally taking values between 1 and >3. Although these differences might be explained by variations in environmental conditions or physical processes organizing the cloud ensembles, the use of improper fitting methods may also introduce large biases. To address this issue, we propose to use a combination of maximum likelihood estimation and goodness‐of‐fit tests to provide more robust power‐law fits while systematically identifying the size range over which these fits are valid. The procedure is applied to cloud size distributions extracted from two idealized high‐resolution simulations displaying different organization characteristics. Overall, power‐laws are found to be outperformed by alternative distributions in almost all situations. When clouds are identified based on a condensed water path threshold, using power‐laws with an exponential cutoff yields the best results as it provides superior fits in the tail of the cloud size distributions. For clouds identified using a combination of water content and updraft velocity thresholds in the free troposphere, no substantial improvement over pure power‐laws can be found when considering more complex two‐parameter distributions. In this context however, exponential distributions provide results that are as good as, if not better than power‐laws. Finally, it is demonstrated that the emergence of scale free behaviors in cloud size distributions is related to exponentially distributed cloud cores merging as they are brought closer to each other by underlying organizing mechanisms.

The Unified Neutral Theory of Biodiversity and Biogeography Revisited

The central question in this review is whether the global and local patterns of biodiversity and abundance distribution dynamics are only subject to general statistical laws, such as these predicted by the Central Limit Theorem (CLT) and Unified Neutral Theory of Biodiversity (UNTB), or whether ecological mechanisms are important too for structuring the biodiversity of our planet. The mathematical foundations of the UNTB appear to rely on some principle of gate-keeping of biological data. An important role of the gate-keeping principle is detected in various biodiversity estimates. Besides, the question has risen whether the ecological dimension of the world’s ecosystems can be adequately described in terms of mathematical distributions and whether alternative abundance distributions are better suited to fit the experimental data. Outline: 1. Introduction: common species and specialists 2. Long distance similarities, Gate-keeping and Biodiversity 3. Statistics for species abundance distributions 4. Pros and Cons of Hubbell’s Unified Neutral Theory of Biodiversity (UNTB) 5. Alternative prospects: towards a (fractal) Global Ecosystem Approach (GEA)

Evaluating generative models in high energy physics

There has been a recent explosion in research into machine-learning-based generative modeling to tackle computational challenges for simulations in high energy physics (HEP). In order to use such alternative simulators in practice, we need well-defined metrics to compare different generative models and evaluate their discrepancy from the true distributions. We present the first systematic review and investigation into evaluation metrics and their sensitivity to failure modes of generative models, using the framework of two-sample goodness-of-fit testing, and their relevance and viability for HEP. Inspired by previous work in both physics and computer vision, we propose two new metrics, the Fr\'echet and kernel physics distances (FPD and KPD, respectively), and perform a variety of experiments measuring their performance on simple Gaussian-distributed, and simulated high energy jet datasets. We find FPD, in particular, to be the most sensitive metric to all alternative jet distributions tested and recommend its adoption, along with the KPD and Wasserstein distances between individual feature distributions, for evaluating generative models in HEP. We finally demonstrate the efficacy of these proposed metrics in evaluating and comparing a novel attention-based generative adversarial particle transformer to the state-of-the-art message-passing generative adversarial network jet simulation model. The code for our proposed metrics is provided in the open source JetNet Python library.

Logistic or not Logistic?

We propose a new class of goodness‐of‐fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization‐based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log‐normal, gamma and chi‐square distributions.

One-Way High-Dimensional ANOVA

ANOVA is one of the most important tools in comparing the treatment means among different groups in repeated measurements. The classical F test is routinely used to test if the treatment means are the same across different groups. However, it is inefficient when the number of groups or dimension gets large. We propose a smoothing truncation test to deal with this problem. It is shown theoretically and empirically that the proposed test works regardless of the dimension. The limiting null and alternative distributions of our test statistic are established for fixed and diverging number of treatments. Simulations demonstrate superior performance of the proposed test over the F test in different settings.

Multiple hypothesis screening using mixtures of non-local distributions with applications to genomic studies.

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian false discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.

Modelling Supra-Classical Logic in a Boltzmann Neural Network: II Incongruence

Abstract Information present in any training set of vectors for machine learning can be interpreted in two different ways, either as whole states or as individual atomic units. In this paper, we show that these alternative information distributions are often inherently incongruent within the training set. When learning with a Boltzmann machine, modifications in the network architecture can select one type of distributional information over the other; favouring the activation of either state exemplar or atomic characteristics. This choice of distributional information is of relevance when considering the representation of knowledge in logic. Traditional logic only utilises preference that is the correlate of whole state exemplar frequency. We propose that knowledge representation derived from atomic characteristic activation frequencies is the correlate of compositional typicality, which currently has limited formal definition or application in logic. Further, we argue by counter-example, that any representation of typicality by ‘most preferred model semantics’ is inadequate. We provide a definition of typicality derived from the probability of characteristic features; based on neural network modelling.

On some aspects of a bivariate alternative zero-inflated logarithmic series distribution

In this paper, we discuss some important aspects of the bivariate alternative zero-inflated logarithmic series distribution (BAZILSD) of which the marginals are the alternative zero-inflated logarithmic series distributions of Kumar and Riyaz (2015. An alternative version of zero-inflated logarithmic series distribution and some of its applications. Journal of Statistical Computation and Simulation, 85(6), 1117–1127). We study some important properties of the distribution by deriving expressions for its probability mass function, factorial moments, conditional probability generating functions, and recursion formulae for its probabilities, raw moments and factorial moments. The parameters of the BAZILSD are estimated by the method of maximum likelihood and certain test procedures are also considered. Further certain real-life data applications are cited for illustrating the usefulness of the model. A simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the BAZILSD.