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In this paper, we present photometric and spectroscopic observations of the subluminous Type Ia supernova (SN Ia) 2012ij, which has an absolute B -band peak magnitude M B , max = âˆ' 17.95 ± 0.15 mag. The B -band light curve exhibits a fast postpeak decline with Î" m 15(B) = 1.86 ± 0.05 mag. All the R - and I / i -band light curves show a weak secondary peak/shoulder feature at about 3 weeks after the peak, like some transitional subclass of SNe Ia, which could result from an incomplete merger of near-infrared (NIR) double peaks. The spectra are characterized by Ti ii and strong Si ii λ 5972 absorption features that are usually seen in low-luminosity objects like SN 1999by. The NIR spectrum before maximum light reveals weak carbon absorption features, implying the existence of unburned materials. We compare the observed properties of SN 2012ij with those predicted by the sub-Chandrasekhar-mass and the Chandrasekhar-mass delayed-detonation models and find that both optical and NIR spectral properties can be explained to some extent by these two models. By comparing the secondary maximum features in the I and i bands, we suggest that SN 2012ij is a transitional object linking normal SNe Ia to typical 91bg-like ones. From the published sample of SNe Ia from the Carnegie Supernova Project II, we estimate that the fraction of SN 2012ijâ€"like SNe Ia is not lower than ∼2%. [ABSTRACT FROM AUTHOR]

This paper presents a family of new continuous wavelet function and describes few properties of it. A method of estimating parameters for a Gaussians using this new continuous wavelet transform is described. The robustness of this method for estimating the parameters in the presence of noise is also studied by simulating different possible cases. [ABSTRACT FROM AUTHOR]

Preferences can vary both across respondents (i.e. inter-respondent preference heterogeneity) and across choice tasks within respondents (i.e. intra-respondent preference heterogeneity). Ignoring the existence of intra-respondent preference heterogeneity could bias preference elicitation and demand forecast. Thus far, most studies covering inter- and intra-respondent preference heterogeneity have applied the mixed multinomial logit model. Meanwhile, the behavioural explanations for such preference variations remain under-explored. This paper accommodates inter- and intra-respondent preference heterogeneity through a two-layer latent class modelling structure, where the continuous random distributions are replaced with discrete mixtures in both layers. A latent variable representing variety-seeking is included to explain class membership probabilities, offering additional behavioural insights concerning the source of preference heterogeneity both across and within respondents. Two aspects associated with variety-seeking are examined: novelty-seeking (i.e. the inclination to adopt new modes) and alternation (i.e. the tendency to vary one's behaviour regularly by selecting different modes continuously). In the context of new shared mobility, this paper finds the role of both aspects in preference heterogeneity. Specifically, novelty seekers are found to be more likely to fall into the class with higher probabilities of switching from existing modes to the new air taxi service than novelty avoiders, and alternation seekers are more likely to belong to the class with higher probabilities to exhibit intra-respondent preference heterogeneity than alternation avoiders. This paper, therefore, provides empirical evidence to identify the target customers of the new air taxi service. [ABSTRACT FROM AUTHOR]

Characterization of a probability distribution gives a unique property enjoyed by that distribution. Various approaches are available in the literature to characterize distributions through record values. Many researchers have characterized Exponential, Pareto, and Power function distributions using moments, conditional expectation, and some other characteristics of record values. In this paper, we have characterized these three distributions through conditional variance of adjacent record values. The results have been verified using numerical computation. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative dual-path planning algorithm rooted in a topological three-dimensional Riemannian manifold (T3DRM) to optimize drone navigation in complex environments. It seamlessly integrates strategies for both discrete and continuous obstacles, employing spherical navigation for the former and hyperbolic paths for the latter. Serving as a transformative tool, the T3DRM facilitates efficient path planning by transitioning between discrete and continuous domains. In uncertain environments with unpredictable obstacle positions, our methodology categorizes these positions as discrete or continuous based on their distribution patterns. Discrete obstacles exhibit random distributions, while continuous obstacles display symmetrical patterns with continuity. Leveraging topological metrics, the T3DRM efficiently classifies these patterns for effective path planning. The findings of this research demonstrate the efficiency of path planning based on classified obstacle positions, enabling swift and efficient drone navigation. This research introduces a pioneering application of a T3DRM, accelerating drone navigation in uncertain environments through a dual approach that simultaneously transforms navigation in primal and dual domains. By enabling spherical and hyperbolic navigation concurrently, the T3DRM offers a comprehensive solution to discrete and continuous path planning challenges. The proposed approach can be used for various indoor applications, especially for warehouse management, surveillance and security, navigation in complex structures, indoor farming, site inspection, healthcare facilities, etc. [ABSTRACT FROM AUTHOR]

This paper explored the concept of past Rényi entropy within the context of k-record values. We began by introducing a representation of the past Rényi entropy for the n-th lower k-record values, sampled from any continuous distribution function F, concerning the past Rényi entropy of the n-th lower k-record values sampled from a uniform distribution. Then, we delved into the examination of the monotonicity properties of the past Rényi entropy of k-record values. Specifically, we focused on the aging properties of the component lifetimes and investigated how they impacted the monotonicity of the past Rényi entropy. Additionally, we derived an expression for the n-th lower k-records in terms of the past Rényi entropy, specifically when the first lower k-record was less than a specified threshold level, and then investigated several properties of the given formula. [ABSTRACT FROM AUTHOR]

The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each wrapped distribution, we state its nth trigonometric moment, mean direction, mean resultant length, skewness, and kurtosis. We also discuss data applications and limitations of each wrapped distribution. This review could be a useful reference and encourage the development of more wrapped distributions. We also mention an R package available for fitting all of the reviewed distributions and illustrate its applications. [ABSTRACT FROM AUTHOR]

In this paper, we recover some traditional results in the geometry of probability distributions, and in particular the convergence of the alternating minimisation procedure, without actually referring to probability distributions. We will do this by discussing a new general concept of two types of points: admissible and agreeable, inspired by multi–agent uncertain reasoning and belief merging. On the one hand, this presents a unique opportunity to make traditional results accessible to a wider audience as no prior knowledge of the topic is required. On the other hand, it allows us to contemplate how a group of rational agents would seek an agreement given their beliefs without necessarily expressing it in terms of probability distributions, focusing instead on logical properties. Finally, we recover Euclidean and Hilbertian settings of discrete and continuous probability distributions. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

The mass fraction of total organic carbon (TOC) is one of the key indicators for evaluating the hydrocarbon generation potential of shale source rocks. Experimental measurements to evaluate the TOC content require significant cost and time. Furthermore, the experimental data are often fragmented and may not provide an accurate depiction of the source rocks throughout the entire block. To solve the above problems, this paper proposes to use the combination of conventional logging data and experimental data after an in-depth study of the geophysical characteristics of hydrocarbon source rocks in the Ordos Basin. A quantitative model between logging data and source rocks is established, and then the continuous distribution value of the TOC content in the hydrocarbon source rock interval is calculated. Firstly, the mud shale formation of the Permian–Shanxi Formation in the Upper Paleozoic, located in the Jingbian area of the Ordos Basin, is selected as the research target using the "Jinqiang method". The model is constructed by selecting appropriate logging curves (acoustic time difference logging, resistivity logging, and density logging) and experimental results based on the response relationship between logging data and TOC data. This method provides more accurate and comprehensive data for source rock studies, combining experimental sampling to contribute to a better evaluation of TOC in source rock. The shale hydrocarbon source rock logging data from 10 wells are selected, and the model is used to realize the full-well section of the logging data to find the hydrocarbon source rock TOC, which is compared with the TOC data from the experimental core tested at a sampling point. The results demonstrate that the model is highly effective and accurate, with a mere 2.7% percentage error observed across 185 sample data points. This method greatly improves the accuracy and completeness of TOC evaluation compared with the results of previous studies and provides a guide for subsequent TOC logging evaluation of source rocks in other areas. With the study in this paper, continuous TOC values of source rocks are obtained, discarding the TOC values representing the whole set of hydrocarbon source rocks with a limited number of sample averages. This method can reflect the contribution of the layers with high and low organic matter abundance, and the calculated reserves are more accurate. By utilizing the measured TOC values of the study area to invert the model to find the parameters, this study contributes to the decision-making of hydrocarbon exploration in domestic and international basins. [ABSTRACT FROM AUTHOR]

The estimation of the slope (b -value) of the frequency–magnitude distribution of earthquakes is based on a formula derived by Aki decades ago, assuming a continuous exponential distribution. However, as the magnitude is usually provided with a limited resolution, its distribution is not continuous but discrete. In the literature, this problem was initially solved by an empirical correction (due to Utsu) to the minimum magnitude, and later by providing an exact formula such as that by Tinti and Mulargia, based on the geometric distribution theory. A recent paper by van der Elst showed that the b -value can be estimated also by considering the magnitude differences (which are proven to follow an exponential discrete Laplace distribution) and that in this case the estimator is more resilient to the incompleteness of the magnitude data set. In this work, we provide the complete theoretical formulation including (i) the derivation of the means and standard deviations of the discrete exponential and Laplace distributions; (ii) the estimators of the decay parameter of the discrete exponential and trimmed Laplace distributions and (iii) the corresponding formulas for the parameter b. We deduce (iv) the standard 1 σ intervals for the estimated b. Moreover, we are able (v) to quantify the error associated with the Utsu minimum-magnitude correction. Furthermore, we have discussed the formulas to produce statistically independent magnitude differences. We tested extensively the b -value estimators on simulated synthetic data sets including complete catalogues as well as catalogues affected by a strong incompleteness degree such as aftershock sequences where the incompleteness is made to vary from one event to the next. We have also analysed the real aftershock sequence of the 30/10/2016 Norcia (central Italy) to integrate the finding of the simulations. To judge the performance of the various estimators we have introduced an index p that can be seen as a non-parametric extension of the Student's t index. The main outcomes of this paper are that (1) the b -value estimators devised for continuous magnitude data are not adequate for binned magnitudes, (2) for complete data sets, estimators based on magnitudes and on magnitude differences provide substantially equivalent results, (3) for incomplete magnitude data sets, estimators based on magnitude differences provide better results and (4) for incomplete aftershock sequences there is no evidence that methods based on positive magnitude differences are superior than other methods using differences. This conclusion is further confirmed by our analysis of the above-mentioned Norcia seismic sequence. This last finding contrasts with the van der Elst's claim that the so called |${{b}_ + }$| method is the most adequate to treat real aftershock sequences. [ABSTRACT FROM AUTHOR]

An extension of the omnibus test statistic of Ebner et al. [A new omnibus test of fit based on a characterization of the uniform distribution. Statistics. 2022;56:1364–1384. doi: 10.1080/02331888.2022.2133121] is considered for the general two-sample alternative. In addition, using the extension this paper introduces a maximum test statistic and an adaptive test statistic for testing the equality of two distributions. The power performance in various situations is investigated for continuous and discrete distributions. Simulation studies based on Monte-Carlo show that the proposed test statistics are good competitors of the existing nonparametric test statistics. The proposed test statistic displays outstanding performance in certain situations, and is illustrated using real data. Finally, we offer some concluding remarks. [ABSTRACT FROM AUTHOR]

This paper introduces a new way to extract a set of representative points from a continuous distribution, which focuses on a method where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when the size of points is small. These points are generated by minimizing the Kullback–Leibler divergence, which is an information-based measure of the disparity between two probability distributions. We refer to these points as Kullback–Leibler points. Based on the link between the total variation and the Kullback–Leibler divergence, we prove that the empirical distribution of Kullback–Leibler points converges to the target distribution. Additionally, we illustrate that Kullback–Leibler points have advantages in simulations when compared with representative points generated by Monte Carlo or other representative points methods. In addition, to prevent the frequent evaluation of complex functions, a sequential version of Kullback–Leibler points is proposed, which adaptively updates the representative points by learning about the complex or unknown functions sequentially. Two potential applications of Kullback-Leibler points in simulation of complex probability densities and optimization of complex response surfaces are discussed and demonstrated with examples. [ABSTRACT FROM AUTHOR]

In this work, we investigate spacings based on order statistics obtained from continuous distribution functions. At the beginning of the paper, we present distributional results for spacings and a method of classification of distributions according to their tails. Then we use this method to derive asymptotic results for spacings. By applying some special versions of Borel–Cantelli lemma, we obtain their strong limit results. At the end of the paper, we present some illustrative examples. [ABSTRACT FROM AUTHOR]

Let F be a continuous distribution function and let Q be its associated quantile function. Let Fh be the kernel estimator of F and Qh that of Q. In this article the L2 right inversion distance between Qh and Q is introduced. It is shown that this distance can be represented in terms of Fh and F, more precisely it is established that the right inversion distance is equal to the conventional integrated squared error between Fh and F. This representation shows that any good bandwidth for Fh is a reasonable bandwidth for Qh and, this fact enables us to suggest methods to choose the smoothing parameter of Q h. Let Q h ̂ c v be the kernel estimator of Q equipped with the global crossvalidation bandwidth h ̂ c v designed for F h. Let Q h ̂ p i be the linear kernel estimator of Q, h ̂ p i being the plug-in bandwidth function. A small scale simulation study presented in this paper contains some examples of distributions for which Q h ̂ c v appears to be superior to Q h ̂ p i . This paper also contains some properties of the classical L2 distance between Qh and Q. [ABSTRACT FROM AUTHOR]

The paper considers the problem of choosing an initial approximation for gradient optimization methods as applied to the inverse problem of restoring the velocity distribution in a heterogeneous continuous medium. The behavior of the medium is described by a system of acoustic equations, and the direct problem is solved by applying a finite-difference scheme. L-BFGS-B is used as a gradient optimization method. The gradient of the error functional with respect to the medium parameters is calculated by applying the adjoint state method. An initial approximation for the gradient method is obtained using a convolutional neural network trained to predict the velocity distribution in a medium from its wave response. It is shown that a neural network trained on responses of simple layered structures can be successfully used to solve the inverse problem for a much more complex Marmousi model. [ABSTRACT FROM AUTHOR]

Sub-bottom profile data have the potential to characterize sediment properties but are seldom used for offshore site investigations because of uncertainties in rock-physics models. Deep-learning techniques appear to be poised to play very important roles in our processing flows for the interpretation of geophysical data. In this paper, a novel deep learning-based method for this task is proposed in which a nonlinear mapping between the observed data and sediment types is learned using a multi-attribute temporal convolution network (MATCN). Firstly, empirical mode decomposition (EMD) is employed for the original data, and intrinsic mode functions (IMFs) with multiple time scales are generated. Based on different IMFs, instantaneous frequency (IF) data under different IMFs can be obtained, while instantaneous phase (IP) and instantaneous amplitude (IA) data are obtained based on the original data. IF, IA and IP data are called attribute data, and are highly related to the attenuation, reflection, and interior structure of the sediment. Thus, IA, IF, and IP are used as the inputs, and a 1D convolutional neural network (CNN) and a time convolution network (TCN) are used to extract sequential features. Different feature representations are then fused. Combining cross-entropy loss function and class-edge loss function, the network is encouraged to produce classified results with more continuous sediment distributions compared with the traditional loss function. The real-data experiments demonstrate that the proposed MATCN has achieved good performance with an F measure greater than 70% in all cases, and greater than 80% in most cases. [ABSTRACT FROM AUTHOR]

The paper introduces the hybrid odd exponential-Φ (HOE-Φ) family, a novel framework for generating a continuous distribution characterized by an additional parameter. The extensive statistical properties of this family are derived and explored in detail. Parameter estimation is performed using the maximum likelihood estimation technique. The efficacy and versatility of the proposed model are demonstrated through a comparative analysis involving two distinct real-world datasets. [ABSTRACT FROM AUTHOR]

Simple Summary: While feeding, the larvae of pygmy moths (Nepticulidae) consume part of a leaf's photosynthetic tissue, thus causing damage to the host plant. Although these insects play a natural role in terrestrial ecosystems, they are perceived as pests in horticulture. This study investigates the identity of a potential Nepticulidae pest infesting plum trees in the Caucasus, initially presumed to be the widespread European Stigmella plagicolella (Stainton). Contrary to expectations, our detailed taxonomic analysis revealed a new species of pygmy moth with distinct male genitalia morphology and molecular differences from its European counterpart. This discovery challenges previous records and highlights the need for accurate pest identification. We hypothesize that the proximity of the Caucasus to Europe emphasizes the importance of monitoring and preventing unintentional pest spread, particularly given potential climate change impacts on the distribution and behavior of pests. Our findings contribute to both practical pest management and scientific understanding of evolutionary processes shaping the Caucasian and European biota. In instances of severe infestations, Nepticulidae larvae can inflict damage on cultivated plants. Previously, it was assumed that the Prunus-feeding Nepticulidae have continuous distribution from Europe to the neighboring Caucasus. During recent fieldwork in the Caucasus, leaf mines were found on plum trees that initially resembled those of Stigmella plagicolella (Stainton) in Europe. However, upon rearing the adults, significant differences emerged, leading to the hypothesis that a different Prunus-feeding species exists in the Caucasus; this challenges previous records in Western Asia. This paper presents the outcomes of our morphological, molecular, and statistical investigations, unveiling S. colchica sp. nov., a previously unknown potential plum-tree pest. Distinguished by male genitalia characteristics, the new species differs from S. plagicolella. The inter- and intraspecific divergences between S. colchica sp. nov. and S. plagicolella range from 3.5% to 6.02%. Moreover, the utilized delimitation algorithms reliably clustered two species separately, as does our mitotype network. A statistical analysis also shows a discernible trend between the leaf mines of S. colchica sp. nov. and S. plagicolella. This unexpected discovery not only documents a new potential pest, enhancing our understanding of the Caucasian fauna, but also contributes to the broader biological inventory. [ABSTRACT FROM AUTHOR]

Supertubes are supersymmetric configurations in string theory in which branes are extending along a closed curve. For a supertube of codimension two, its dipole charge is characterized by the duality monodromy around the closed curve. When multiple codimension-2 supertubes are present, the monodromies around different supertubes can be non-commuting, namely non-Abelian. Non-Abelian configurations of supertubes are expected to play an important role in non-perturbative physics of string theory, especially black holes. In this paper, in the framework of five-dimensional supergravity, we construct exact solutions describing codimension-2 supertubes in three-dimensional space. We use an extension formula to construct a three-dimensional solution from a two-dimensional seed solution. The two-dimensional seed is an F-theory like configuration in which a torus is nontrivially fibered over a complex plane. In the first example, there is a stack of circular supertubes around which there is a non-trivial monodromy. In some cases this can be thought of as a microstate of a black hole in AdS2 × S2. The second example is an axi-symmetric solution with two stacks of circular supertubes with non-Abelian monodromies. In addition, there is a continuous distribution of charges on the symmetry axis. [ABSTRACT FROM AUTHOR]

In reliability studies, we are interested in the behaviour of a system when it interacts with its surrounding environment. To assess the system's behaviour in a reliability sense, we can take the system's intrinsic quality as strength and the outcome of interactions as stress. Failure is observed whenever stress exceeds strength. Taking Y as a random variable representing the stress the system experiences and random variable X as its strength, the probability of not failing can be taken as a proxy for the reliability of the component and given as P (Y < X) = 1 − P (X < Y) . This way, in the present paper, it is considered that X and Y follow generalized extreme value distributions, which represent a family of continuous probability distributions that have been extensively applied in engineering and economic contexts. Our contribution deals with a more general scenario where stress and strength are not independent and copulas are used to model the dependence between the involved random variables. In such modelling framework, we explored the proper selection of copula models characterizing the dependence structure. The Gumbel–Hougaard, Frank, and Clayton copulas were used for modelling bivariate data sets. In each case, information criteria were considered to compare the modelling capabilities of each copula. Two economic applications, as well as an engineering one, on real data sets are discussed. Overall, an easy-to-use methodological framework is described, allowing practitioners to apply it to their own research projects. [ABSTRACT FROM AUTHOR]

The problem of optimal estimation of location and scale parameters of absolutely continuous distributions, by means of two-dimensional confidence regions based on L-statistics, is considered. The case, when the sample size is random and tends to infinity, is studied. The paper can be considered as a supplement to Zaigraev and Alama-Bućko (Metrika 81:283–305, 2018) in case of samples of random size. [ABSTRACT FROM AUTHOR]

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy. [ABSTRACT FROM AUTHOR]

The rainfall distribution in southwest China is uneven, and the rainstorm threshold cannot use in a unified standard. This paper synthesizes a calculation method for the extremely heavy precipitation threshold and the provision of the rainstorm threshold in meteorological operation. It calculates the daily precipitation rainstorm threshold at 400 national ground stations in southwest China. The rainstorm events from 1961 to 2021 were statistically analyzed using the rainstorm threshold and analyzing the spatial-temporal variation characteristics. The results show that the number of single-station rainstorm events and the average precipitation of single-station rainstorm events in southwest China decreased from east to west. The number and frequency of single-station rainstorm events in Guizhou, Sichuan, Tibet, and Chongqing are increasing, while the number of single-station rainstorm events in Yunnan is decreasing. There is no apparent spatial distribution pattern for the continuous rainstorm events in the southwest region. From 1961 to 2021, the number and frequency of rainstorm events at a single station in southwest China followed an upward trend. The number of rainstorm events at a single station increased by 16.7 times · (10a)−1, and the frequency of rainstorms increased by 9.9% · (10a)−1. The continuous rainstorm events show an increasing trend, with an increase of 0.1 times · (10a)−1. Using the rainstorm threshold in southwest China, the early warning threshold for rainstorm disasters can be adjusted. The temporal and spatial characteristics of rainstorm events since 1961 can analyze the changes occurring in rainstorm events under global warming and provide data to support the response of southwest China to climate change. [ABSTRACT FROM AUTHOR]

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The challenges of point cloud registration in intelligent vehicle driving lie in the large scale, complex distribution, high noise, and strong sparsity of lidar point cloud data. This paper proposes an efficient registration algorithm for large-scale outdoor road scenes by selecting the continuous distribution of key area laser point clouds as the registration point cloud. The algorithm extracts feature descriptions of the key point cloud and introduces local geometric features of the point cloud to complete rough and fine registration under constraints of key point clouds and point cloud features. The algorithm is verified through extensive experiments under multiple scenarios, with an average registration time of 0.5831 s and an average accuracy of 0.06996 m, showing significant improvement compared to other algorithms. The algorithm is also validated through real-vehicle experiments, demonstrating strong versatility, reliability, and efficiency. This research has the potential to improve environment perception capabilities of autonomous vehicles by solving the point cloud registration problem in large outdoor scenes. [ABSTRACT FROM AUTHOR]

This paper investigates the compress-and-forward scheme for an uplink cloud radio access network (C-RAN) model, where multi-antenna base stations (BSs) are connected to a cloud-computing-based central processor (CP) via capacity-limited fronthaul links. The BSs compress the received signals with Wyner-Ziv coding and send the representation bits to the CP; the CP performs the decoding of all the users’ messages. Under this setup, this paper makes progress toward the optimal structure of the fronthaul compression and CP decoding strategies for the compress-and-forward scheme in the C-RAN. On the CP decoding strategy design, this paper shows that under a sum fronthaul capacity constraint, a generalized successive decoding strategy of the quantization and user message codewords that allows arbitrary interleaved order at the CP achieves the same rate region as the optimal joint decoding. Furthermore, it is shown that a practical strategy of successively decoding the quantization codewords first, then the user messages, achieves the same maximum sum rate as joint decoding under individual fronthaul constraints. On the joint optimization of user transmission and BS quantization strategies, this paper shows that if the input distributions are assumed to be Gaussian, then under joint decoding, the optimal quantization scheme for maximizing the achievable rate region is Gaussian. Moreover, Gaussian input and Gaussian quantization with joint decoding achieve to within a constant gap of the capacity region of the Gaussian multiple-input multiple-output (MIMO) uplink C-RAN model. Finally, this paper addresses the computational aspect of optimizing uplink MIMO C-RAN by showing that under fixed Gaussian input, the sum rate maximization problem over the Gaussian quantization noise covariance matrices can be formulated as convex optimization problems, thereby facilitating its efficient solution. [ABSTRACT FROM PUBLISHER]

In this paper, we study a new type of distribution that generalizes distributions from the gamma and beta classes that are widely used in applications. The estimators for the parameters of the digamma distribution obtained by the method of logarithmic cumulants are considered. Based on the previously proved asymptotic normality of the estimators for the characteristic index and the shape and scale parameters of the digamma distribution constructed from a fixed-size sample, we obtain a statement about the convergence of these estimators to the scale mixtures of the normal law in the case of a random sample size. Using this result, asymptotic confidence intervals for the estimated parameters are constructed. A number of examples of the limit laws for sample sizes with special forms of negative binomial distributions are given. The results of this paper can be widely used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support. [ABSTRACT FROM AUTHOR]

Multi-layer particle bed has an important application in the field of high temperature filtration. This paper uses the Discrete Element Method to study the flow and segregation characteristics of multi size mixed particles on inclined surfaces. The research results show that: in the process of segregation, the particles mainly carry out rolling motion; when the replacement rate of the particles reaches 60%, the degree of segregation reaches the maximum, and the optimal incline length is 600 mm. A universal quantification index for particle bed segregation and a criterion for the steady state of particle flowing are obtained. The particle size distribution close to continuous distribution is not conducive to particle segregation. The segregation effect of the largest and smallest particles in the mixed particles is better than that of the intermediate particles. This study provides a reference for the design of the segregation layered structure of the multi size particle bed. A universal quantization index for particle segregation was proposed The criterion of steady state and critical replacement rate were given The critical value of slant length for ternary particle segregation was obtained The unique mechanism in the process of segregation of multi-particle size was obtained The multi size particles segregation law based on size distribution was determined [ABSTRACT FROM AUTHOR]

Quantile regression and quantile treatment effect methods are powerful econometric tools for considering economic impacts of events or variables of interest beyond the mean. The use of quantile methods allows for an examination of impacts of some independent variable over the entire distribution of continuous dependent variables. Measurement in many quantitative settings in economic history have as a key input continuous outcome variables of interest. Among many other cases, human height and demographics, economic growth, earnings and wages, and crop production are generally recorded as continuous measures, and are collected and studied by economic historians. In this paper we describe and discuss the broad utility of quantile regression for use in research in economic history, review recent quantitative literature in the field, point to potential limits in its use, and provide an illustrative example of the use of these methods based on 20,000 records of human height measured across 50-plus years in the 19th and 20th centuries. We suggest that, despite limitations in certain settings, there is still considerably more room in the literature on economic history to convincingly and productively apply quantile regression methods. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a bivariate distribution on R + × N arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on R + × N and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective EM algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models. [ABSTRACT FROM AUTHOR]

In this paper, the unit Garima distribution is introduced. It is used for analysing proportional data. Some statistical properties of the proposed distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measures. A new family of continuous distributions, called the unit Garima-generated family of distributions, is also provided. It used the unit Garima distribution as the main generator. Some sub-models of the unit Garima-generated family of distributions are provided, such as the unit Garima-beta, unit Garima-Weibull, and unit Garima-normal distributions. The method of maximum likelihood is used to estimate the model parameters. A Monte Carlo simulation is used to illustrate the performance of the percentile confidence interval construction for each parameter of the proposed distributions. Finally, the developed distributions are applied to eight real data sets. [ABSTRACT FROM AUTHOR]

This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann's alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form [ G (·) ] λ , where λ > 0 and G (·) is a continuous cumulative distribution function. This mixture can be useful in economics, financial, and actuarial fields, where extreme and long tails appear in the empirical data. The special case in which G (·) is the Stoppa cumulative distribution function, which is a good description of the random behaviour of large losses, is studied in detail. We provide properties of this mixture, mainly related to the analysis of the tail of the distribution that makes it a candidate for fitting actuarial data with extreme observations. Inference procedures are discussed and applications to three well-known datasets are shown. [ABSTRACT FROM AUTHOR]

This paper aims to introduce robot technology to carry out the safety inspection of transmission towers in long-distance power transmission, so as to improve the safety and efficiency of inspection. However, aiming at the problem that the existing climbing robots are mainly used for large load applications, which leads to the large size and lack of flexibility of the robot, we propose an innovative solution. Firstly, a lightweight quadruped climbing robot is designed to improve portability and operational flexibility. Then, a one-dimensional force sensor is added at the end of each leg of the robot, and a special swing phase trajectory is designed. The robot can judge whether the electromagnetic adsorption is effective and avoid potential safety hazards. Finally, based on the principle of virtual model control (VMC), a foot-end force balancing algorithm is proposed to achieve uniform distribution and continuous change in force, and improve safety and load capacity. The experiments show that the scheme has a stable climbing ability in the environments of angle steel, vertical ferromagnetic plane and transmission tower. [ABSTRACT FROM AUTHOR]

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typically provide continuous distribution. Recently, the functional expansion tally (FET) and kernel density estimation (KDE) methods have been developed to provide a continuous distribution of a Monte Carlo tally. In this paper, we propose a method to estimate a continuous distribution of a quantity in all phase-space variables using a fully connected feedforward artificial neural network (ANN) model with Monte Carlo-based training data. As a proof of concept, a continuous distribution of iterated fission probability (IFP) was estimated by ANN models in two distinct fissile systems. The ANN models were trained on the training data created using the Monte Carlo IFP method. The estimated IFP distributions by the ANN models were compared with the Monte Carlo-based data that include the training data. Additionally, the IFP distributions by the ANN models were also compared with the adjoint angular neutron flux distributions obtained with the deterministic neutron transport code PARTISN. The comparisons showed varying degrees of agreement or discrepancy; however, it was observed that the ANN models learned the general trend of the IFP distributions from the Monte Carlo-based training data. [ABSTRACT FROM AUTHOR]

In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called "tpn", has been implemented, which includes the relevant cases of interest in this family. [ABSTRACT FROM AUTHOR]

This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution. [ABSTRACT FROM AUTHOR]

Recently, the uncertainty aspects of record values have been increasingly studied in the literature. In this paper, we study the residual Tsallis entropy of upper record values coming from random samples. In the continuous case, we define the Tsallis entropy quantity for the residual lifetime of upper record values in general distributions as the residual Tsallis entropy of upper record values coming from a uniform distribution. We also obtain a lower bound on the residual Tsallis entropy of upper data set values originating from an arbitrary continuous probability distribution. We also discuss the monotonic property of the residual Tsallis entropy of upper data sets. [ABSTRACT FROM AUTHOR]

In probability theory, there are discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions with infinite supports. We discuss some asymptotic behaviors of convolution powers of the Riemann zeta distribution. [ABSTRACT FROM AUTHOR]

By definition, original Besag-conceived spatial auto-random variables incorporate an autoregressive spatial lag term (i.e., the sum/average of nearby attribute values) to characterize geospatial data. Very common variates include the auto-normal, auto-logistic, and auto-binomial; less common ones include the auto-beta and auto-multinomial. Some of these specifications can capture the full range of spatial autocorrelation, and others cannot. These latter variates are unorthodox in their nonconformist restrictions to either only positive or only negative spatial autocorrelation domains. The literature already offers successful modifications of the auto-Poisson and auto-negative binomial, two popular random variables for describing counts, but neither of which can encapsulate positive spatial autocorrelation. The literature dismissively mentions the auto-exponential variate, which cannot accommodate negative spatial autocorrelation situations. Meanwhile, the literature lacks any discussion about auto-uniform random variables, with implications especially from point pattern analysis publications that they solely refer to complete spatial randomness. The purpose of this paper is to postulate a productive and viable spatialized continuous uniform distribution specification that easily extends to its corresponding discrete version. A standard benchmark location-allocation simulation experiment for a simple p = 1 median problem, a spatial optimization circumstance that illuminates bivariate spatial median properties, illustrates its practical applicability. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the notion of continuous *-frames and *-C-controlled frames in Hilbert C*-modules. We present some results of continuous frames in the view of *-Ccontrolled frames in Hilbert C*-modules. Also we define *-(C,C')- frames and investigate multiplier operators for these frames. [ABSTRACT FROM AUTHOR]

In this paper additive partial linear models with generalized log-gamma errors and P-spline smoothing are proposed for uncensored data. This class derived from the generalized gamma distribution contains various continuous asymmetric distributions to the right and to the left with domain on the real line and has the normal distribution as a particular case. The location parameter is modeled in a semiparametric way so that one has a generalized gamma accelerated failure time additive partial linear model. A joint iterative process is derived, that combines the penalized Fisher scoring algorithm for estimating the parametric and nonparametric regression coefficients and a quasi-Newton procedure for obtaining the scale and shape estimates. Discussions on the inferential aspects of the former estimators as well as on the derivation of the effective degrees of freedom are given. Diagnostic procedures are also proposed, such as residual analysis and sensitivity studies based on the local influence approach. Simulation studies are performed to assess the empirical distributions of the parametric and nonparametric estimators and a real data set on personal injury insurance claims made in Australia from January 1998 to June 1999 is analyzed by the methodology developed through the paper. Technical results, tables, graphs, R codes and the data set used in the application are presented as Supplementary Materials. [ABSTRACT FROM AUTHOR]

A new class of statistics obtained by ordering the absolute values of the observations arising from absolutely continuous distributions which are symmetrically distributed about zero is introduced in this paper. The statistics generated by the above method are named as absolved order statistics (AOS) of the given sample. The association of the distribution of these statistics with the distribution of order statistics arising from the folded form of the parental density about zero is outlined. The vector of AOS is proved to be a minimal sufficient statistic for the class F θ (1) of all absolutely continuous distributions which are symmetrically distributed about zero. A method of estimation of the scale parameter of any distribution belonging to F θ (1) using AOS is described. Illustration on the advantage of the above method of estimation is described for the distributions such as (i) logistic, (ii) normal, and (iii) double Weibull. A more realistic censoring scheme involving AOS as well is discussed in this paper. We have derived the U-statistic estimator based on AOS for the scale parameter σ of any distribution f (x , σ) ∈ F θ (1) using the best linear unbiased estimate (BLUE) based on AOS of a preliminary sample as kernel. We have illustrated the performance of this estimator with an U-statistic generated from BLUE based on order statistics for each of (i) logistic (ii) normal and (iii) double Weibull distributions. [ABSTRACT FROM AUTHOR]

In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index S pmk is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the S pmk is also studied. The asymptotic confidence interval is also constructed for S pmk . The simulation results indicate that estimators for both the unknown parameters of the new distribution and the S pmk provide reasonable results. Some practical analyses are also performed on both the new distribution and the S pmk . The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for S pmk illustrate that the new distribution can be utilized for process capability indices by quality controllers. [ABSTRACT FROM AUTHOR]

Nested simulation has been an active area of research in recent years, with an important application in portfolio risk measurement. While majority of the literature has been focusing on the continuous case where portfolio loss is assumed to follow a continuous distribution, monetary losses of a portfolio in practice are usually measured in discrete units, oftentimes due to the practical consideration of meaningful decimal places for a given level of precision in risk measurement. In this paper, we study a nested simulation procedure for estimating conditional Value-at-Risk (CVaR), a popular risk measure, in the case where monetary losses of the portfolio take discrete values. Tailored to the discrete nature of portfolio losses, we propose a rounded estimator and show that when the portfolio loss follows a sub-Gaussian distribution or has a sufficiently high-order moment, the mean squared error (MSE) of the resulting CVaR estimator decays to zero at a rate close to Γ − 1 , much faster than the rate of the CVaR estimator in the continuous case which is Γ − 2 / 3 , where Γ denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples. [ABSTRACT FROM AUTHOR]

In analyzing bivariate data sets, data with common observations are frequently encountered and, in this case, existing absolutely continuous bivariate distributions are not applicable. Only a few models, such as the bivariate distribution proposed by Marshall and Olkin (J Am Stat Assoc 62(317):30–44, 1967), have been developed to model such data sets and the choice of models to fit data sets having common observations is very limited. In this paper, three general classes of bivariate distributions for modeling data with common observations are developed. To develop the bivariate distributions, we employ a probability model in reliability. Considering a system with two components, it is assumed that, when the first failure of the components occurs, with some probability, it immediately causes the failure of the remaining component, and, with complementary probability, the residual lifetime of the remaining component is shortened according to some stochastic order. It will be shown that, by specifying the underlying distributions contained in the joint distribution, numerous families of bivariate distributions can be generated. Therefore, this work provides substantially increased flexibility in modeling data sets with common observations. The developed models are fitted to two real-life data sets and it is shown that these models outperform the existing models in terms of fitting performance and their performances are satisfactory. [ABSTRACT FROM AUTHOR]

Simultaneous testing of one hypothesis at multiple alpha levels can be performed within a conventional Neyman-Pearson framework. This is achieved by treating the hypothesis as a family of hypotheses, each member of which explicitly concerns test level as well as effect size. Such testing encourages researchers to think about error rates and strength of evidence in both the statistical design and reporting stages of a study. Here, we show that these multi-alpha level tests can deliver acceptable expected total error costs. We first present formulas for expected error costs from single alpha and multiple alpha level tests, given prior probabilities of effect sizes that have either dichotomous or continuous distributions. Error costs are tied to decisions, with different decisions assumed for each of the potential outcomes in the multi-alpha level case. Expected total costs for tests at single and multiple alpha levels are then compared with optimal costs. This comparison highlights how sensitive optimization is to estimated error costs and to assumptions about prevalence. Testing at multiple default thresholds removes the need to formally identify decisions, or to model costs and prevalence as required in optimization approaches. Although total expected error costs with this approach will not be optimal, our results suggest they may be lower, on average, than when "optimal" test levels are based on mis-specified models. [ABSTRACT FROM AUTHOR]