The Generalized Poisson Distribution (GPD) adds an extra parameter to the usual Poisson distribution. This parameter induces a loss of homogeneity in the stochastic processes modeled by the distribution. Thus, the generalized distribution becomes an useful model for counting processes where the occurrence of events is not homogeneous. This model creates the need for an inferential procedure, to test for the value of this extra parameter. The FBST (Full Bayesian Significance Test) is a Bayesian hypotheses test procedure, capable (...) of providing an evidence measure on sharp hypotheses (where the dimension of the parametric space under the null hypotheses is smaller than that of the full parametric space). The goal of this work is study the empirical properties of the FBST for testing the nullity of extra parameter of the generalized Poisson distribution. Numerical experiments show a better performance of FBST with respect to the classical likelihood ratio test, and suggest that FBST is an efficient and robust tool for this application. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It (...) is shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

Báo Khoa học & Phát triển ngày 23-2 đăng một bài ngắn nhưng thú vị và rất giá trị của TS Phạm Hiệp, viết về trải nghiệm và suy ngẫm qua nhận biết những phát kiến mới, nhỏ (nhưng “hạt tiêu”) trong công việc nghiên cứu khoa học.Bài viết rõ ràng phản ánh một dáng điệu tăng trưởng tư duy trong tổng thể tiếp cận nhận thức luận, một trong ba trụ cột quan trọng của triết học khoa học. Trong (...) bài viết ngắn để tiếp dòng suy nghĩ của TS Phạm Hiệp, bàn tiếp về tính “động” của thể trạng nhỏ (từ quan sát “tĩnh”) là việc đáng làm, tôn tạo tiếp giá trị bài vừa nói trên Khoa học và Phát triển. Qua đó, chân dung của thực tế tương lai có thể sẽ rất khác, mặc dù chỉ bắt đầu nho nhỏ mà thôi. (shrink)

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated (...) solution in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package. (shrink)

The data analyzed in this paper are part of the results described in Bueno et al. (2000). Three cytogenetics endpoints were analyzed in three populations of a species of wild rodent – Akodon montensis – living in an industrial, an agricultural, and a preservation area at the Itajaí Valley, State of Santa Catarina, Brazil. The polychromatic/normochromatic ratio, the mitotic index, and the frequency of micronucleated polychromatic erythrocites were used in an attempt to establish a genotoxic profile of each area. It (...) was assumed that the three populations were in the same conditions with respect to the influence of confounding factors such as animal age, health, nutrition status, presence of pathogens, and intra- and inter-populational genetic variability. Therefore, any differences found in the endpoints analyzed could be attributed to the external agents present in each area. The statistical models used in this paper are mixtures of negative-binomials and Poisson variables. The Poisson variables are used as approximations of binomials for rare events. The mixing distributions are beta densities. The statistical analyzes are under the bayesian perspective, as opposed to the frequentist ones often considered in the literature, as for instance in Bueno et al. (2000). (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Credit risk, also known as default risk, is the likelihood of a corporation losing money if a business partner defaults. If the liabilities are not met under the terms of the contract, the firm may default, resulting in the loss of the company. There is no clear way to distinguish between organizations that will default and those that will not prior to default. We can only make probabilistic estimations of the risk of default at best. There are two types of (...) credit risk default models in this regard: structural and reduced-form models. Structural models are used to calculate the likelihood of a company defaulting based on its assets and liabilities. If the market worth of a company's assets is less than the debt it owes, it will default. Reduced form models often assume an external cause of default, such as a Poisson jump process, which is driven by a stochastic process. They model default as a random event with no regard for the balance sheet of the company. This paper provides a Review of credit risk default models. (shrink)

This article studies the quantum effect of the brain neuronal system on both normal and abnormal conscious states. It develops Plasma Brain Dynamics (PBD) to obtain a set of kinetic quantum-plasma Wigner-Poisson equations. The model is established under typical electrostatic and collision-free conditions in both the absence and presence of an external magnetic field. The quantum perturbation is solved analytically by employing a backward-mapping approach to the motion of electrons. Results expose that the quantum perturbation turns out to be (...) zero at normal conscious states; but no more than 11% of the classical perturbation under assumed abnormal situations like a sudden head trauma, mood disorder, etc. The introduction of the magnetic field does not influence the results. (shrink)

In this note, we consider a Merton model for default risk, where the firm’s value is driven by a Brownian motion and a compound Poisson process.

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the ℏ→0 limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, (...) we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the ℏ→0 case) on the fiber C*-algebras. (shrink)

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these (...) structures are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us (...) a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread. (shrink)

The paper presents, a new large deviations principles (SLDP) of non-Freidlin-Wentzell type, corresponding to the solutions Colombeau-Ito’s SDE. Using SLDP we present a new approach to construct the Bellman function ????(????, ????) and optimal control ????(????, ????) directly by way of using strong large deviations principle for the solutions Colombeau-Ito’s SDE. As important application such SLDP, the generic imperfect dynamic models of air-to-surface missiles are given in addition to the related simple guidance law. A four, examples have been illustrated proposed (...) approach and corresponding numerical simulations have been illustrated and analyzed. Using SLDP approach, Jumps phenomena, in financial markets, also is considered. Jumps phenomena, in financial markets is explained from the first principles, without any reference to Poisson jump process. In contrast with a phenomenological approach we explain such jumps phenomena from the first principles, without any reference to Poisson jump process. (shrink)

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that general relativity theory may be reduced to the Newton's gravity theory in the limit of a weak gravitational field and slow motion of the material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations to Newton's equation of motion and Poisson's gravitational potential equation, respectively, is scrutinized and proven to be mathematically, physically and dimensionally (...) wrong and also the geometrization of gravity is not really necessary. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

Credit risk, also known as default risk, is the likelihood of a corporation losing money if a business partner defaults. If the liabilities are not met under the terms of the contract, the firm may default, resulting in the loss of the company. There is no clear way to distinguish between organizations that will default and those that will not prior to default. We can only make probabilistic estimations of the risk of default at best. There are two types of (...) credit risk default models in this regard: structural and reduced form models. Structural models are used to calculate the likelihood of a company defaulting based on its assets and liabilities. If the market worth of a company's assets is less than the debt it owes, it will default. Reduced form models often assume an external cause of default, such as a Poisson jump process, which is driven by a stochastic process. They model default as a random event with no regard for the balance sheet of the company. This paper provides a Review of credit risk default models. (shrink)