Search

This paper aims to investigate the behavior of LiMgN half-Heusler (HH) semiconductor doped by transition metals (TM  =  Mn, Fe, Co and Ni). HHs belong to the F 4 ̄ 3 m space group (No. 216) and have a zinc blende structure that can be described by the chemical symbol XYZ. The research methodology utilized in this investigation involves theoretical analysis based on the principles of density functional theory (DFT). The studied LiMg 0. 9 5 TM 0. 0 5 N alloy displayed the half-metallicity behavior when TM  =  Fe, Co and Ni. Hence, these systems could be a promising candidate in spintronic application thanks to their ferromagnetism. The principal contribution to magnetism in the full LiMg 0. 9 5 TM 0. 0 5 N alloys comes from the Mn, Fe, Co and Ni doping. The partial magnetic moments of these elements are significantly greater than the combined partial magnetic moments of Li, Mg and N. When comparing LiMg 0. 9 5 Mn 0. 0 5 N to LiMg 0. 9 5 Fe 0. 0 5 N, 5Co 0. 0 5 N and LiMg 0. 9 5 Ni 0. 0 5 N, it is important to note that the exchange splitting energy Δ (e + , e −) TM associated to their spin up and spin down were discussed. The variation of Mn(3d) in relation to ( e + , e − ) is larger than that of Fe, Co and Ni. Therefore, Δ (e + , e −) Mn > Δ (e + , e −) Fe > Δ (e + , e −) Co > Δ (e + , e −) Ni . Furthermore, there is a correlation between the magnetic moment and electronegativity trend of the TM dopant. Specially, the electronegativity trend ( χ TM ) is well matched with the total spin moment trend, where χ Ni > χ Co > χ Fe > χ Mn . [ABSTRACT FROM AUTHOR]

Let f be a holomorphic Hecke eigenform of S L 2 (Z) with weight k. Denote by L(s, f) the automorphic L-function attached to f, and S (t , f) = 1 π arg L (1 2 + i t , f) , where the argument is obtained by continuous variation along the straight line { s ∈ C | ℜ s ≥ 1 2 , ℑ s = t } , starting with the value 0 at infinity. Here, a new zero density estimate of L(s, f) in short intervals is achieved. As an application, the integral moment of S(t, f) is obtained, i.e., for l ∈ Z + and sufficiently large T, ∫ T T + H | S (t , f) | 2 l d t = (2 l) ! l ! (2 π) 2 l H (log log T) l + O (H (log log T) l - 1 2 ) holds for T 15 16 + ε ≤ H ≤ T , which improves the previous result. [ABSTRACT FROM AUTHOR]

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr‐Hatke, and discrete inverted Topp–Leone distributions. [ABSTRACT FROM AUTHOR]

This study introduces the family of the novel "cot-generator" distributions based on the cotangent function. The construction of the probability density function based on the cot-generator and its corresponding moments, reliability indicators, and order statistics are derived. Regarding inferential procedures, the maximum likelihood estimation method is implemented to estimate the model parameters in a non-closed form. The novel Cot-Fréchet distribution (NCFD) is then focused on a specific class member, constructed using the Fréchet distribution as the baseline. The estimators' bias, variance, and mean square error (MSE) efficiency are examined and evaluated through Monte Carlo simulation experiments. The novel model is also applied to some real data sets to assess its efficacy and is compared with other competing distributions. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternative distribution to model count data exhibiting uni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined by a parametric weight function that admits up to two modes for the resulting probability mass function. Like the baseline beta-binomial distribution, the proposed distribution performs well in modeling overdispersed binomial data. Structural properties of the new distribution are studied. Raw moments are derived, which are used to describe the dispersion behavior relative to the mean and the skewness behavior. Parameter estimation is carried out using the maximum likelihood method. A simulation study is conducted in order to illustrate the behavior of the estimators. Finally, two applications illustrating the usefulness of the proposal are presented. [ABSTRACT FROM AUTHOR]

In this study, a new two-parameter discrete distribution is introduced by mixing Poisson and Quasi-Shanker distributions. The new model is named Poisson Quasi-Shanker-(PQS) distribution. Some important mathematical properties of the proposed distribution are derived including factorial moments, moment-generating function, variance, and dispersion index. The parameters of PQS distribution are estimated using the maximum likelihood estimation approach. A Monte Carlo simulation is carried out to illustrate the behavior of derived estimators. The applicability of the new model is assessed using two datasets from different areas. It is concluded the proposed distribution is more flexible as compared to the considered competitive distributions. [ABSTRACT FROM AUTHOR]

In this study, an improved extension of the Haq distribution was introduced. The new model is named "size-biased Haq distribution (SBHD)". Its two special cases length-biased and area-biased Haq distribution are discussed. The important mathematical properties such as moments, moment generating function, variance, skewness, kurtosis, Rényi entropy, survival function, hazard function, and mean residual life are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study was utilized to illustrate the behavior of derived estimators. Two datasets from different fields are utilized to illustrate the flexibility of the new distributions. It is concluded that the new model is more flexible and efficiently analyzed when the datasets are compared to the considered competitive distributions. [ABSTRACT FROM AUTHOR]

There are exponential operators which are defined on the whole real line, namely, the Ismail–May operators (Tnf)(x)$$ \left({T}_nf\right)(x) $$, connected to 1+x2$$ 1+{x}^2 $$, and the Gauss–Weierstrass operators (Wnf)(x)$$ \left({W}_nf\right)(x) $$, connected with 1. Here we consider the composition Vn:=Tn∘Wn$$ {V}_n:= {T}_n\circ {W}_n $$ of these two operators and observe that the composition operator is not of exponential type operator. We find moment‐generating functions and moments of these operators and estimate some point‐wise convergence of these operators using the characteristic function. We also estimate quantitative Voronovskaya type asymptotic formula and error estimation. Also, the difference of the composition operators Vn$$ {V}_n $$ with its components Tn$$ {T}_n $$ and Wn$$ {W}_n $$ is estimated in terms of modulus of continuity. Finally, we provide some graphs to see visualize the convergence by considering the function x2e2x$$ {x}^2{e}^{2x} $$. [ABSTRACT FROM AUTHOR]

AbstractRecently, considerable interest has been in deriving explicit expressions for moment of different truncated multivariate distributions. This is due to their usefulness in developing efficient EM-algorithm for the maximum likelihood estimation of the corresponding distributional parameters. One rich family of distributions is the multivariate normal mean-mixture distribution as it includes a number of important multivariate distributions as special cases. In this article, we derive exact expressions for the first two moments of doubly truncated multivariate normal mean-mixture distributions, from which results for various special cases are then deduced. [ABSTRACT FROM AUTHOR]

We investigate exponential sums modulo primes whose phase function is a sparse polynomial, with exponents growing with the prime. In particular, such sums model those which appear in the study of the quantum cat map. While they are not amenable to treatment by algebro‐geometric methods such as Weil's bounds, Bourgain gave a nontrivial estimate for these and more general sums. In this work, we obtain explicit bounds with reasonable savings over various types of averaging. We also initiate the study of the value distribution of these sums. [ABSTRACT FROM AUTHOR]

In this article we, proposed a new two parameter distribution called inverted power modified Lindley distribution. The main objective is to introduce an extension to inverted modified Lindley distribution as an alternative to the inverted exponential, inverted gamma and inverted modified Lindley distributions, respectively. The proposed distribution is more flexible than the above mentioned distributions in terms of its hazard rate function. In the part of estimation of the proposed model, we first utilize the maximum likelihood (ML) estimator and parametric bootstrap confidence intervals, viz., standard bootstrap, percentile bootstrap, bias-corrected percentile (BCPB), bias-corrected accelerated bootstrap (BCAB) from the classical point of view as well the Bayesian estimation under different loss functions, squared error loss function, modified squared error loss function, and Bayes credible interval as to obtain the model parameter based on order statistics. A simulation study is carried out to check the efficiency of the classical and the Bayes estimators in terms of mean squared errors and posterior risks, respectively. Two real life data sets, have been analyzed for order statistics to demonstrate how the proposed methods may work in practice. [ABSTRACT FROM AUTHOR]

This paper introduces and discusses the novel asymmetric class of distributions that have the name inverse power Lomax power series (IPLPS). This class of distributions is produced by combining the inverse power Lomax with the power series distributions. This combined approach provides an opportunity for the creation of flexible distributions with significant physical implications in many fields, like biology and engineering. The IPLPS distributions encompass several new compound distributions as sub-models along with a new class of compound distributions. Many statistical features, including moments, quantile function, conditional moments, inverse moments, uncertainty measures, and probability-weighted moments, are obtained. As a special model of the generated class, the parameters of the inverse power Lomax Poisson distribution are estimated by different methods, including least squares, Cramér von Mises, maximum likelihood, and weighted least squares. Through an extensive simulation analysis, the execution of different parameter estimation techniques for the inverse power Lomax Poisson model is performed to show its validity based on its mean squared error and absolute bias. Two real datasets are utilized to show the practicality of the newly generated model. Results show that the inverse power Lomax Poisson distribution provides the most fitted model for these datasets in comparison to other distributions such as power Lomax, Marshall-Olkin power Lomax, power Lomax Poisson, and Topp-Leone Lomax distributions. [ABSTRACT FROM AUTHOR]

This paper introduces a new statistical distribution called length biased quasi suja distribution (LBQS). It explores its properties, including moments, moment generating function(MGF), characteristic function(CF), harmonic mean, reliability, hazard rate and reverse hazard rate. Order statistics of the above distribution is obtained. Furthermore, the paper also examines various entropy which measures the randomness of system, like Renyi entropy and Tsalli's entropy. It also evaluates Bonferroni and Lorenz curves which are useful in measuring the inequality. It also discusses parameter estimation techniques specifically maximum likelihood estimation and likelihood ratio testing. Moreover, a simulation study has been conducted to demonstrate how well the distribution would perform in real-life situation. The validity of the distribution is also demonstrated with real-world data example of failure data, highlighting its potential for practical applications in data analysis. [ABSTRACT FROM AUTHOR]

Moment representations have been proposed to facilitate the interpretation of geophysical time domain electromagnetic responses. We present a new methodology for estimating these moments from field data for different system waveforms when on-time and off-time measurements are available. Quadrature impulse response moments are estimated by a recursive relation involving moments of the input waveform and moments of the observed response. After adapting this method to time domain electromagnetic applications—in particular, MEGATEM and AeroTEM (AirTEM) airborne electromagnetic systems—we present the results from applying this method on synthetic and real data collected over the Reid–Mahaffy test site in northern Ontario, Canada. [ABSTRACT FROM AUTHOR]

The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced, consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented. [ABSTRACT FROM AUTHOR]

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular, we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper. [ABSTRACT FROM AUTHOR]

A novel distribution family named the Transmuted Odd Moment Exponential-G (TOME-G) family is introduced, derived from both the Odd Moment Exponential-G and Transmuted families. Within this family, three distinct models are proposed: the transmuted odd moment exponential Lomax (TOMEL) distribution, transmuted odd moment exponential Rayleigh (TOMER) distribution, and transmuted odd moment exponential exponential (TOMEE) distribution. The density function shape for each model, such as symmetric or asymmetric (including right-skewed, left-skewed, increasing, decreasing, and uni-modal), is discussed. Key statistical characteristics of the family, including the expansion of the probability density function (PDF), moments, incomplete moment, Mo generating function, residual life, and reversed residual life functions, are derived. Additionally, three estimation methods—maximum likelihood estimation (MLE), Ordinary Least Squares Estimator (OLSE), and Weighted Least Squares Estimator (WLE)—are examined for estimating model parameters. A simulation study is conducted to compare the performance of these estimation methods. We covered two real-life applications in this study, both involving life tests. One of them is in the engineering domain, aiming to study the time to failure between manufactured units. The other application is in the medical field, focusing on leukemia data for life tests.

In this study, a new two-parameter discrete distribution is introduced by mixing Poisson and Quasi-Shanker distributions. The new model is named Poisson Quasi-Shanker-(PQS) distribution. Some important mathematical properties of the proposed distribution are derived including factorial moments, moment-generating function, variance, and dispersion index. The parameters of PQS distribution are estimated using the maximum likelihood estimation approach. A Monte Carlo simulation is carried out to illustrate the behavior of derived estimators. The applicability of the new model is assessed using two datasets from different areas. It is concluded the proposed distribution is more flexible as compared to the considered competitive distributions.

In this study, an improved extension of the Haq distribution was introduced. The new model is named “size-biased Haq distribution (SBHD)”. Its two special cases length-biased and area-biased Haq distribution are discussed. The important mathematical properties such as moments, moment generating function, variance, skewness, kurtosis, Rényi entropy, survival function, hazard function, and mean residual life are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study was utilized to illustrate the behavior of derived estimators. Two datasets from different fields are utilized to illustrate the flexibility of the new distributions. It is concluded that the new model is more flexible and efficiently analyzed when the datasets are compared to the considered competitive distributions.

Recent studies have discussed the application and relevance of trigonometry in probability distributions. In this paper, a new, trigonometric family of distributions derived from the alliance of the families known as Sine-G and Generalized G family, inspiring the name Sine Generalized-G Family is proposed and studied. The characteristics of the distribution are explained through the mode, stochastic ordering, quantile function, expansion of the distributional function, and moment. A sub-model of the family named Sine generalized Inverse Gompertz (SG-IG) distribution was studied, its parameters estimated using non-Bayesian and Bayesian procedures. Rigorous simulation studies involving the utilization of the Metropolis–Hasting (MH) algorithm in the Monte Carlo Markov Chain (MCMC) algorithm was carried out to determine the efficiency of the methods and the usefulness was illustrated using two real datasets. The method of Weighted Least squares (WLS) was found to be more efficient in the estimation of parameters of the SG-IG distribution using the lifetime data compared to its competitors.

In this work we study positivity preservers T : R [ x 1 , ... , x n ] → R [ x 1 , ... , x n ] with constant coefficients and define their generators A if they exist, i.e., exp ⁡ (A) = T. We use the theory of regular Fréchet Lie groups to show the first main result. A positivity preserver with constant coefficients has a generator if and only if it is represented by an infinitely divisible measure (Main Theorem 4.7). In the second main result (Main Theorem 4.11) we use the Lévy–Khinchin formula to fully characterize the generators of positivity preservers with constant coefficients. [ABSTRACT FROM AUTHOR]

Let f be a Gaussian random field on R d and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has finite moments. So far, this has been established only for moments of order lower than three. In this paper, we prove the conjecture. Precisely, we show that X has finite moment of order p, as soon as, at any given point, the Taylor polynomial of order p of f is non-degenerate. We present a simple and general approach that is not specific to critical points and we provide various applications. In particular, we show the finiteness of moments of the nodal volumes and the number of critical points of a large class of smooth, or holomorphic, Gaussian fields, including the Bargmann-Fock ensemble. [ABSTRACT FROM AUTHOR]

We construct and study properties of an infinite dimensional analog of Kahane's theory of Gaussian multiplicative chaos (Kahane in Ann Sci Math Quebec 9(2):105-150, 1985). Namely, if H T (ω) is a random field defined w.r.t. space-time white noise B ˙ and integrated w.r.t. Brownian paths in d ≥ 3 , we consider the renormalized exponential μ γ , T , weighted w.r.t. the Wiener measure P 0 (d ω) . We construct the almost sure limit μ γ = lim T → ∞ μ γ , T in the entire weak disorder (subcritical) regime and call it subcritical GMC on the Wiener space. We show that μ γ { ω : lim T → ∞ H T (ω) T (ϕ ⋆ ϕ) (0) ≠ γ } = 0 almost surely, meaning that μ γ is supported almost surely only on γ -thick paths, and consequently, the normalized version is singular w.r.t. the Wiener measure. We then characterize uniquely the limit μ γ w.r.t. the mollification scheme ϕ in the sense of Shamov (J Funct Anal 270:3224–3261, 2016) – we show that the law of B ˙ under the random rooted measure Q μ γ (d B ˙ d ω) = μ γ (d ω , B ˙) P (d B ˙) is the same as the law of the distribution f ↦ B ˙ (f) + γ ∫ 0 ∞ ∫ R d f (s , y) ϕ (ω s - y) d s d y under P ⊗ P 0 . We then determine the fractal properties of the measure around γ -thick paths: - C 2 ≤ lim inf ε ↓ 0 ε 2 log μ ^ γ (‖ ω ‖ < ε) ≤ lim sup ε ↓ 0 sup η ε 2 log μ ^ γ (‖ ω - η ‖ < ε) ≤ - C 1 w.r.t a weighted norm ‖ · ‖ . Here C 1 > 0 and C 2 < ∞ are the uniform upper (resp. pointwise lower) Hölder exponents which are explicit in the entire weak disorder regime. Moreover, they converge to the scaling exponent of the Wiener measure as the disorder approaches zero. Finally, we establish negative and L p ( p > 1 ) moments for the total mass of μ γ in the weak disorder regime. [ABSTRACT FROM AUTHOR]

We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a consequence, using the Stein and cumulant methods we derive Berry-Esseen bounds for the asymptotic convergence of renormalized k-hop path counts to the normal distribution as the density of Poisson vertices tends to infinity. Computer codes for the recursive symbolic computation of moments and cumulants of any orders are provided as an online resource. [ABSTRACT FROM AUTHOR]

Abstract This research introduces a novel two-parameter distribution, the power-modified XLindley distribution, developed through the application of power transformation techniques to the existing modified XLindley distribution. This new distribution enhances flexibility and adaptability in statistical modeling. We conduct a thorough examination of its statistical properties, exploring its potential to improve data fitting and modeling accuracy. To assess the effectiveness of the model, we employ multiple estimation techniques and evaluate their performance through extensive simulation experiments. Our findings indicate that the maximum product of the spacings method is particularly effective for parameter estimation. To demonstrate the practical utility of the proposed model, we apply it to two real-world datasets: one related to flood data and the other to reliability engineering. The results underscore the distribution’s superior ability to capture the characteristics of these datasets compared to existing models, highlighting its significance for applications in natural disaster analysis and reliability studies.

This article proposes a new way to increase the flexibility of a family of statistical distributions by adding two additional parameters. The newly proposed family is called the alpha–beta power transformation family of distributions. A specific model, the alpha–beta power exponential distribution, was thoroughly investigated. The hazard rates of the proposed distribution can be decreasing, bathtub-shaped, and unimodal. The derived structural features of the proposed model include explicit formulations for the quantiles, the moments, the moment-generating function, and the incomplete and conditional moments. In addition, estimates of maximum likelihood, least squares, weighted least squares, and minimum distance of Cramér von Mises, von Anderson–Darling, and right-tail Anderson–Darling are obtained for the unknown parameters. Two real data sets were examined to demonstrate the usefulness of the proposed approach.

Since standard distributions do not fundamentally have an acceptable fit to all types of data sets, it is necessary to construct extensions of standard distributions to increase their capability in data modeling. As a result of this shortage in old ones, we proposed a novel generator based on the trigonometric function (Arctan). We selected the Frechet distribution as the baseline for the generator’s applicability. This generator produces the “new Arctan Frechet distribution” (NATFD). The fundamental properties of the proposed distribution have been taken into consideration. Estimating the given distribution’s parameters is accomplished using the maximum-likelihood method. A simulation study is carried out to evaluate the superiority of the proposed distribution, and two actual data sets are used.

Subject and Purpose. A new method for detecting narrow band interferences is discussed, with the use of an example record of Jovian Io-C decametric radio storm as obtained with the UTR-2 array on April 10, 2020. We aimed at developing an efficient and simple algorithm based on a detailed analysis of the effect the radio interference environment and the frequency response of the telescope may have on the efficiency of the interference mitigation procedure. Methods and Methodology. The ‘orthogonal detection’ method proposed for identifying linear interference patterns in dynamic spectra of powerful radio sources has been adapted for application to narrow band interferences of various spectral widths and variable brightness, which often happen to be located close to (or intersect with) the signal of interest. In order to minimize the impact of the telescope’s frequency response, a discretized frequency-scanning technique is used, which permits a steady approximation of the averaged spectrum by low order polynomials, as well as removal of the frequency trend which hinders distinguishing between the low-level interference signals and those coming from the source. Results. An efficient approach to the problem of detecting long lasting, narrowband interference's in dynamical spectra (conditionally stationary interferences) is proposed. The algorithm has been tested on the example of a powerful storm of Jovian radio emission. The proposed technique can be especially useful in situations where the signal of interest overlaps with the interference in the time-frequency domain. Conclusions. The new approach to the problem of interference mitigation, based on the development of combined algorithms of signal separation in the time-frequency domain, has been shown to offer an effective method of signal processing. In contrast to the previously used methods based on calculation of statistical moments for amplitudes, the new approach allows avoiding use of the same statistical indicators for both interference detection and subsequent steps of data analysis intended for building physical models and interpreting the observational data.

Abstract We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.

Recently, the need to develop statistical distributions has become the most important spot. In this context, we employ the α‐power transformation (APT) method to convert the generalized Pareto distribution (GPD) into a new distribution. Some statistical properties of the proposed distribution are being studied, such as moments, arithmetic mean, moment‐generating function, random variables, entropy, reliability, and hazard function (HF). In addition, the proposed distribution is compared with the Pareto distribution and some other forms of alpha power distributions, such as the alpha power Pareto (APP) distribution, alpha power Rayleigh (APR) distribution, and the alpha power Lomax (APL) distribution. Finally, we demonstrate the benefits of the proposed distribution through a simulation study and two real data sets. It was found that the results showed the MLE method is reliable, the APTGP distribution is a competitive distribution for the aforementioned data set, and it is a mirror image of the Pareto distribution. [ABSTRACT FROM AUTHOR]

We introduce a new flexible distribution four-parameter which is called [0,1]Truncated Exponentiated Exponential Burr type X distribution ([0,1] TEE-BX). Using binomial series expansion and exponential expansion, the new distribution is expanded by four parameters. We derive moments, moment generating function, quantile function, order statistics and the Rényi entropy. The maximum likelihood estimation method is used to estimate the parameters of the proposed TEE-BX model [0,1]. Finally, using two real-world data sets, the performance of the [0,1] TEE-BX distribution is explored. Based on the certain goodness of fit criteria, we conclude that the [0,1] TEE-BX distribution has a better fit than the other distributions. [ABSTRACT FROM AUTHOR]

Methods of modelling the female torso during physical activity often neglect the position and movement of the breast. This novel investigation compares three female torso modelling approaches that differ in complexity (integrated breast, fixed breast, dynamic breast) to determine the effect on spinal joint moments during running and jumping. The commonly used integrated breast model distributed breast mass within the torso, the fixed breast model attached the mass of the breasts to fixed positions on the anterior of the torso, and a new dynamic breast model enabled relative motion between the breasts and anterior torso. Key findings demonstrated minimal differences in lumbar spine moments (<0.05 Nm/kg; 4%) between integrated breast and fixed breast models but greater differences, up to 0.86 Nm/kg (68%) during running and 0.89 Nm/kg (82%) during jumping, when breast motion was included. Thoracic spine moments revealed similar patterns with minimal differences (<0.05 Nm/kg; 11%) between integrated breast and fixed breast models and greater differences, up to 0.48 Nm/kg (92%) during running and 0.63 Nm/kg (66%) during jumping, with the dynamic breast model. Future female musculoskeletal models should consider including breast mass and motion to avoid mis-representing spinal loading in females during running and jumping. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified Bernstein-type operators based on two real parameters and study its various approximation properties. We derive some direct results e.g. Voronovkaja type asymptotic theorem, an estimate of error in ordinary as well as in Ditzian Totik modulus of smoothness and an error estimate for functions belonging to the Lipschitz type space. Further, we examine the rate of approximation for a Kirov and Popova type generalization of these operators. [ABSTRACT FROM AUTHOR]

This article proposes a new way to increase the flexibility of a family of statistical distributions by adding two additional parameters. The newly proposed family is called the alpha–beta power transformation family of distributions. A specific model, the alpha–beta power exponential distribution, was thoroughly investigated. The hazard rates of the proposed distribution can be decreasing, bathtub-shaped, and unimodal. The derived structural features of the proposed model include explicit formulations for the quantiles, the moments, the moment-generating function, and the incomplete and conditional moments. In addition, estimates of maximum likelihood, least squares, weighted least squares, and minimum distance of Cramér von Mises, von Anderson–Darling, and right-tail Anderson–Darling are obtained for the unknown parameters. Two real data sets were examined to demonstrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

Since standard distributions do not fundamentally have an acceptable fit to all types of data sets, it is necessary to construct extensions of standard distributions to increase their capability in data modeling. As a result of this shortage in old ones, we proposed a novel generator based on the trigonometric function (Arctan). We selected the Frechet distribution as the baseline for the generator's applicability. This generator produces the "new Arctan Frechet distribution" (NATFD). The fundamental properties of the proposed distribution have been taken into consideration. Estimating the given distribution's parameters is accomplished using the maximum-likelihood method. A simulation study is carried out to evaluate the superiority of the proposed distribution, and two actual data sets are used. [ABSTRACT FROM AUTHOR]

The main object of this paper is to introduce generalized Mittag-Leffler type Poisson distribution. We obtain results regarding moments about the origin, Moment generating function, probability generating function and characteristic function for this distribution. It should be worthy to note that the above results reduce to corresponding results of Mittag-Leffler type Poisson distribution and Poisson distribution for specific values of parameters. [ABSTRACT FROM AUTHOR]

We study the 2k-th moment of central values of the family of Dirichlet L-functions to a fixed prime modulus. We establish sharp lower bounds for all real k ≥ 0 and sharp upper bounds for k in the range 0 ≤ k ≤ 1 . [ABSTRACT FROM AUTHOR]

Although it is very easy to calculate the 1st moment and 2nd moment values of the geometric distribution with the methods available in existing books and other articles, it is quite difficult to calculate moment values larger than the 3rd order. Because in order to find these moment values, many higher order derivatives of the geometric series and convergence properties of the series are needed. The aim of this article is to find new formulas for characteristic function of the geometric random variable (with parameter p) in terms of the Apostol–Bernoulli polynomials and numbers, and the Stirling numbers. This characteristic function characterizes the geometric distribution. Using the Euler's identity, we give relations among this characteristic function, the Apostol–Bernoulli polynomials and numbers, and also trigonometric functions including cosine and sine. A relations between the characteristic function and the moment generating function is also given. By using these relations, we derive new moments formulas in terms of the Apostol–Bernoulli polynomials and numbers. Moreover, we give some applications of our new formulas. [ABSTRACT FROM AUTHOR]

The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, Ln,s,q, introduced by L. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that Ln,s,q possesses n -- s + 1 linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted. [ABSTRACT FROM AUTHOR]

Over numerous decades, academics have been attempting to develop a number of novel distributions to satisfy certain realistic demands. The rationale is that conventional distributions have generally been shown to lack fit in actual applications, such as medicinal research, engineering, hydrology, environmental science, and many more. Combining the Weibull and inverse Nadarajah Haghighi distributions generates a novel life-time distribution with four parameters, which is referred to as the Weibull-inverse Nadarajah Haghighi (WINH) distribution. Different structural characteristics of the formulated distribution have been determined and analysed. Distinct plots depict the behaviour of the probability density function (pdf) and the cumulative distribution function (cdf). The maximum likelihood estimation method is applied to estimate the stated distribution parameters. To assess and investigate the efficacy of estimators in terms of bias, variance, and mean square error (MSE), a simulation study was conducted. Lastly, the effectiveness of the stated distribution is proven by actual data sets. [ABSTRACT FROM AUTHOR]

In this paper, we establish the expected order of magnitude of the k th-moment of central values of the family of Dirichlet L -functions to a fixed prime modulus over function fields for all real k ≥ 0. [ABSTRACT FROM AUTHOR]

In this paper, we study the combinatorial relations between the cokernels cok ⁡ (A n + p ⁢ x i ⁢ I n ) ( 1 ≤ i ≤ m ), where A n is an n × n matrix over the ring of p-adic integers ℤ p , I n is the n × n identity matrix and x 1 , ... , x m are elements of ℤ p whose reductions modulo p are distinct. For a positive integer m ≤ 4 and given x 1 , ... , x m ∈ ℤ p , we determine the set of m-tuples of finitely generated ℤ p -modules (H 1 , ... , H m) for which (cok ⁡ (A n + p ⁢ x 1 ⁢ I n ) , ... , cok ⁡ (A n + p ⁢ x m ⁢ I n )) = (H 1 , ... , H m) for some matrix A n . We also prove that if A n is an n × n Haar random matrix over ℤ p for each positive integer n, then the joint distribution of cok ⁡ (A n + p ⁢ x i ⁢ I n ) ( 1 ≤ i ≤ m ) converges as n → ∞ . [ABSTRACT FROM AUTHOR]

The generalized hyperbolic distributions are fast becoming the most popular models for financial returns. In recent years, many variants of generalized hyperbolic distributions have been proposed in the literature. This paper provides a review of generalized hyperbolic and related distributions, including software available for them. A simulation study and real data applications are presented to compare some of the reviewed distributions. [ABSTRACT FROM AUTHOR]

Dial M for Simulation For years, systems of stochastic differential equations (SDEs) were simulated by discretization, inevitably introducing a bias, which can be difficult to quantify accurately. To circumvent this, some attempts have been made to simulate exactly various models from the SDE solution. These approaches prove capable of producing accurate results. A serious drawback of such an approach, nevertheless, is the implicit need to use extensive numerical methods, which make the entire simulation computationally heavy and quite impracticable. In the paper "Unified moment-based modeling of integrated stochastic processes," Kyriakou, Brignone, and Fusai present a methodological framework based on M(oments) for the simulation of such models that overcomes earlier limitations. Theoretical results and extensive numerical experiments show that the proposed approach allows accurate simulation of complex stochastic models with low computational effort. In this paper, we present a new method for simulating integrals of stochastic processes. We focus on the nontrivial case of time integrals, conditional on the state variable levels at the endpoints of a time interval through a moment-based probability distribution construction. We present different classes of models with important uses in finance, medicine, epidemiology, climatology, bioeconomics, and physics. The method is generally applicable in well-posed moment problem settings. We study its convergence, point out its advantages through a series of numerical experiments, and compare its performance against existing schemes. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2422. [ABSTRACT FROM AUTHOR]

We consider time-inhomogeneous Hawkes processes with an exponential kernel, and we analyze some properties of the model. Time-inhomogeneity for the Hawkes process is indispensable for short rate models or for other calibration purposes, while financial applications for the time-homogeneous case already well known. Distributional properties for such a model generate computational tractability for a financial application. In this paper, moments and the Laplace transform of time-inhomogeneous Hawkes processes are obtained from the distributional properties of the underlying processes. As an applications to finance, we investigate the pricing formula for zero-coupon bonds when short-term interest rates are governed by the time-inhomogeneous Hawkes process. Numerical illustrations are also provided. As an illustrative example, we apply the derived moments and Laplace transform of time-inhomogeneous Hawkes processes to the pricing of zero-coupon bonds within a financial context. By considering the short-term interest rate as driven by inhomogeneous Hawkes processes, we develop explicit formulae for valuing zero-coupon bonds. This application is particularly relevant for modeling interest rate dynamics in real-world scenarios, allowing for a more nuanced understanding of pricing dynamics. Through numerical illustrations, we demonstrate the computational tractability of our approach, showcasing its practical utility for financial practitioners and providing insights into the intricate interplay between time-inhomogeneous Hawkes processes and bond pricing in dynamic markets. [ABSTRACT FROM AUTHOR]

This article introduces the generalized Kumaraswamy power Lindley (GKPL) distribution, a novel probabilistic model derived by combining the generalized Kumaraswamy (GK-G) family with the power Lindley (PL) distribution. The GKPL distribution encompasses a wide range of distributions, including Kumaraswamy power Lindley, Kumaraswamy Lindley, generalized power Lindley, generalized Lindley, power Lindley, and the well-known Lindley, as special cases. Fundamental properties are derived, such as the hazard rate function, survival function, quantile function, reverse hazard function, moments, mean residual life function, entropy, and order statistics. To determine the parameters of the GKPL distribution, four estimation methods, including maximum likelihood, least squares, Cramer-von Mises, and AndersonDarling methods, are used to estimate the parameters of the GKPL distribution. The effectiveness of the estimation techniques is assessed by employing Monte Carlo simulations. The adaptability and validity of the proposed GKPL distribution are compared with alternative models, including the Kumaraswamy power Lindley (KPL), Extended Kumaraswamy power Lindley (EKPL), type II generalized Topp Leone-power Lindley (TIIGTLPL), exponentiated generalized power Lindley (EGPL), generalized Kumaraswamy Weibull (GKW), generalized Kumaraswamy log-logistic (GKLLo), and generalized Kumaraswamy generalized power Gompertz (GKGPGo) distributions, through analyses of three real datasets. [ABSTRACT FROM AUTHOR]

We introduce a new unified extension of the integral form of Euler's beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer's confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function. [ABSTRACT FROM AUTHOR]

In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little‐known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture. [ABSTRACT FROM AUTHOR]

Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs. [ABSTRACT FROM AUTHOR]

In this study, a novel distribution called the Extended-Lomax distribution which generalizes the existing Lomax distribution and has increasing and decreasing shapes for the hazard rate function was proposed. Various structural properties of the new proposed distribution are derived including the survival function, hazard function, and rth moment. The probability density function (PDF) plots indicated that the distribution is skewed to the right. To estimate the parameters of the newly proposed distribution, two estimation methods which include the Maximum likelihood approach and Method of Moments was employed. The main objective of the proposed distribution's construction was to increase the adaptability of the current Lomax distributions so that they could better suit reliability data sets than alternative candidate distributions with an equivalent number of parameters. This distribution should be able to eliminate the Heavy-tail of the current distribution and model both monotonic and non-monotonic patterns of failure rates. Solar photovoltaic system reliability data was used to evaluate the performance of the proposed Extended Lomax distribution as well as the estimation methods. [ABSTRACT FROM AUTHOR]