Use of Probabilistic Approaches to Predict Cash Deficits

This article deals with issues related to the use of mathematical methods of cash deficit probability predictions. A number of objective and subjective factors are described that prevent the wide integration of mathematical methods in the practical activities of economists. It is justified that, due to the large number of external and internal factors affecting the economic system state, the values of indicators of an economic system state are often random. The possibility of using probability theory methods to predict the occurrence of cash deficits is proved. Using empirical data including the results of thousands of observations, the possibility of using the normal distribution density function for the purpose of predicting insufficient funds for payment is illustrated. The essence of the proposed model is that it contains a prediction of a macrotrend—i.e., the risk of a cash gap—based on high-frequency microlevel data. At the same time, a prediction of the probability of a cash deficit, and not its estimation for a specific date, was made. This is the main difference between the described model and common scoring estimates. This article proposes an approach to estimate the probability of a cash deficit based on data from a specific business entity, rather than aggregated data from other organizations.

Polynomials, numerical triangles and sequences associated with the probability distribution of the hyperbolic cosine type for odd values of the parameter

The article introduces a new class of polynomials that first appeared in the probability distribution density function of the hyperbolic cosine type. With an integer change in one of the parameters of this distribution, polynomials in the form of a product of positive factors are written out with an increasing degree. Earlier, the author found a connection between the distribution of the hyperbolic cosine type and numerical sets, in particular, in the simplest cases with the triangle of coefficients of Bessel polynomials, the triangle of Stirling numbers, sequences of coefficients in the expansion of various functions, etc. Also from the distribution formed numerous numerical sequences, both new and widely known. Consideration of polynomials separately from the density function made it possible to reconstruct numerical sets of coefficients, ordered in the form of numerical triangles and numerical sequences. The connections between the elements of the sets are established. Among the sequences obtained, in the simplest cases, there are those known from others, for example, physical problems. However, the overwhelming majority of the found number sets have not been encountered earlier in the literature. The obvious applications of this research are number theory and algebra. And the interdisciplinarity of the results indicates the possibility of applications and enhances their practical significance in other areas of knowledge.

Polynomials and number sets associated with the probability distribution of the hyperbolic cosine type for even values of the parameter

The polynomials used in the formation of the probability distribution density function of the hyperbolic cosine type are investigated. Earlier, on the basis of a hyperbolic cosine distribution, the author obtained numerical sets, among which not only new ones, but also, for example, the triangle of Stirling numbers, the triangle of the coefficients of Bessel polynomials, sequences of coefficients in the expansion of various functions, etc. In this paper, depending on the natural parameter m and the real distribution parameter β , a new class of polynomials is obtained. For even and odd m , the polynomials are constructed using similar, but different formulas. The article presents polynomials for even values m . Structurally, polynomials consist of quadratic factors. The coefficients of the polynomials, ordered by m , form numerical triangles depending on β . Some relations are found between the coefficients. From the numerical triangles, a set of numerical sequences is obtained, which for integers β are integers. Also, polynomials with respect to x turn out to be polynomials with respect to β . With this interpretation the variable acts as a parameter. New numerical triangles and sequences for different x were found. The overwhelming majority of the obtained numerical sequences are new. The class of polynomials arising from problems of probability theory indicates the possibility of applying the results.

Strategy of efficient estimation of soil organic content at the local scale based on the national spectral database

The aim of this paper was to compare the prediction performance of three strategies: general global Partial least squares regression (PLSR) using CSSL with and without spiking samples, memory-based learning (MBL) using CSSL with and without spiking samples and general PLSR using only spiking samples to predict soil organic matter in the target area. When using spiked subsets, we also investigated the prediction performance of the extra-weighted subsets. A series of spiking subsets randomly selected from the total spiking samples were selected by conditioned Latin hypercube sampling (cLHS) from the target sites. We calculated the mean squared Euclidean distance (msd) of different spiking subsets with the distribution density function of their vis–NIR spectra only and statistically inferred the optimal sampling set size to be 30. Our study showed that when the number of spiking were lower than 30, the predicted accuracy derived from global PLSR using CSSL spiked with and without extra-weighted samples was greater than the predicted accuracy derived from the general PLSR using the corresponding number of spiking samples only (RMSE 5.57–5.98 v.s. RMSE 6.76). Global PLSR using CSSL spiked with the statistically optimal local samples can achieve higher predicted performance (with a mean RMSE of 5.75). MBL spiked with five extra-weighted optimal spiking samples achieved the best accuracy with an RMSE of 3.98, an R2 of 0.70, a bias of 0.04 and an LCCC of 0.81. The msd is a simple and effective method to determine an adequate spiking size using only vis–NIR data.

Diagnostics of impregnation defects of reinforcing filaments of polymer composite with built-in fibre-optic sensor with distributed Bragg grating

Mathematical model of unidirectional fibrous polymer composite material with optical fiber sensor built into reinforcing fiber (filament of elementary fibers) with distributed Bragg grating is developed in order to diagnoste defects of filament impregnation - finding probability of impregnation defect as relative length of local sections of filament without impregnation, i.e. without filling binder of space between its elementary fibers. The technique of digital processing of reflection spectrum according to the solution of the integral Fredholm equation of the 1st kind is used in order to find the desired informative function of density of distribution of axial strains along the length of the sensitive section of the fibre-optic sensor. The approach assumes that the optical fiber sensor is embedded in the composite material at the stage of its manufacture, wherein the low-reflective nature of the sensitive portion of the optical fiber allows linear summation of reflection coefficients from its various local portions regardless of their mutual positions. Algorithm of numerical processing of strain distribution density function is developed for finding of sought probability of presence of impregnation defects along filament length. It has been revealed that the distribution density function has pronounced informative pulses, from the location and value of which the sought-after values of probability of presence of impregnation defects along the length of the filament can be found. The results of diagnostics of different values of the sought probability of the filament impregnation defect are presented based on the results of numerical simulation of the measured reflection spectra and the sought function of strain distribution density along the length of the sensitive section of the optical fiber sensor at different values of the volume fraction of the filaments, combinations of transverse and longitudinal loads of the representative domain of the unidirectional fibrous composite material in comparison with graphs for the case without load.

Computational aspects of finite-frequency traveltime inversion kernels

Finite-frequency traveltime inversion offers higher accuracy for velocity model building than ray-based traveltime inversion. The adjoint force is the key to computation of inversion kernels. Starting at the definition of inversion kernels for the acoustic wave equation, we derive the explicit formula for the spectral distribution density function used in the adjoint force computation. Two formulations are provided for the computation of adjoint forces for receiver-side extrapolation, frequency-domain representation and time-domain representation. The accuracy of finite-frequency traveltime inversion kernels is benchmarked with the analytical solutions for homogeneous isotropic media. We use wavefront construction to compute the first Fresnel zones for kernel conditioning. Based on dynamic ray tracing, we design a processing procedure guided by synthetic data tests to extract the desired events for wavefield backward extrapolation from the data. Unlike ray-based velocity tomography, finite-frequency inversion can resolve the velocity structures comparable with the size of Fresnel zones as we demonstrate on a marine salt model using ocean bottom node acquisition geometry. Despite the fact that the inversion kernels are based on Born approximation, velocities with errors up to 20% can be well resolved. For practical purposes, a simple formulation is given for the determination of the shot spacing. The proposed workflow for finite-frequency inversion is efficient and converges only in very few iterations.

Experimental Investigation of Stochastic Mechanical Behavior of Cement Emulsified Asphalt Mortar under Monotonic Compression

Experimental investigation on cement emulsified asphalt mortar (CA mortar) under uniaxial monotonic compression by taking into account the stochastic properties were investigated. An analytical constitutive model based on the statistic damage approach capable of mimicking the stochastic mechanical responses of CA mortar under uniaxial compression was proposed. The comparison between the experimental results and the predictions demonstrated that the proposed model was able to characterize the salient features for CA mortar under uniaxial monotonic compression. Furthermore, the compressive stochastic evolution (SE) of CA mortar tested in this work and comparative analyses among typical China Railway Track System-I (CRTS-I) type CA mortar and concrete in several aspects were examined and performed; it was revealed that the Lognormal distribution density function can well represent the damage probability density for CA mortar, and its stochastic constitutive relationship can be reflected by a media process of transition from microscale to macroscale.