In this note we discuss the development of a new Gamma exponentiated functional GE ( α , h ) distribution, using the Gamma baseline distribution generating method by Zografos and Balakrishnan. The raw moments of the Gamma exponentiated functi...
The purpose of this work is to provide applications of real, complex, and functional analysis to moment, interpolation, functional equations, and optimization problems. Firstly, the existence of the unique solution for a two-dimensional full Markov m...
The properties of the unique nontrivial analytic solution, defined implicitly by a functional equation, are pointed out. This work provides local estimations and global inequalities for the involved solution. The corresponding operatorial equation is...
A direct way to estimate the likelihood and magnitude of extreme events is frequency analysis. This analysis is based on historical data and assumptions of stationarity, and is carried out with the help of probability distributions and different meth...
Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used....
This paper provides a simplified representation of the exact density function of R, the sample correlation coefficient. The odd and even moments of R are also obtained in closed forms. Being expressed in terms of generalized hypergeometric functions,...
Time-dependent reliability analysis (TRA) is essential for the life-cycle risk assessment of engineering systems. However, existing TRA methods often require extensive statistical data or computationally expensive surrogate models, which limit their...
The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in t...
Knee osteoarthritis (KOA) is an age-dependent disease dominantly affected by mechanical loading. Balancing the forces acting on the medial knee compartment has been the focus of KOA interventions. This pilot study investigated the effects of function...
An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear...
Moment invariants have been extensively studied and widely used in object recognition. The pioneering investigation of moment invariants in pattern recognition was due to Hu, where a set of moment invariants for similarity transformation were develop...
In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd We...
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas fo...
In this article, a discrete analogue of an extension to a two-parameter half-logistic model is proposed for modeling count data. The probability mass function of the new model can be expressed as a mixture representation of a geometric model. Some of...
Reliability analysis of complex engineering products often involves high-dimensional nonlinear state functions, with random variable distributions hard to determine due to limited samples, restricting the fourth-order moment method that fails to link...
Knowable moments, abbreviated as K-moments, are redefined as expectations of maxima or minima of a number of stochastic variables that are a sample of the variable of interest. The new definition enables applicability of the concept to any type of va...
The family of stable distributions and, in particular, the α-stable distribution increases its applicability in engineering sciences. Examination of industrial data shows that originally assumed Gaussian properties are not so often observed. Re...
This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is dis...
The main aim of this paper is to define and investigate a new class of symmetric beta type distributions with the help of the symmetric Bernstein-type basis functions. We give symmetry property of these distributions and the Bernstein-type basis func...
In this work, a novel generalized family of distributions called the odd beta prime is introduced. The linear representations of the proposed family are obtained. The expressions for the moments, the moment-generating function, and entropy are derive...
In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical an...
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 aggregation ability and exciton dynamics of dyes are largely affected by properties of the dye monomers. To facilitate aggregation and improve excitonic function, dyes can be engineered with substituents to exhibit optimal key properties, such as...
In the present study, abilities of various macroscopic models (Navier–Stokes–Fourier, Burnett, original and regularized Grad’s 13-moment equations) in predicting the nonequilibrium molecular velocity distribution are examined. The r...
The fourth-moment method can accurately perform a reliability analysis when it is challenging to determine the distribution of the random variable due to limited available samples. This method only utilizes the first four moments of the random variab...
The confluent hypergeometric beta distribution due to Gordy has been known since the 1990s, but not much of is known in terms of its mathematical properties. In this paper, we provide a comprehensive treatment of mathematical properties of the conflu...
In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the...
Approximate analytical methods have been frequently used in geotechnical engineering to estimate the reliability of geotechnical structures due to their efficiency and simplicity. The main spirit of these methods is using the moments of the limit sta...
Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments. In this situation the theory of Differential e...
Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a genera...
We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorem...
Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2,Z) and let L(s,sym2f)=∑n=1∞cnn−s,ℜs>1 denote the symmetric square L-function of f. In this paper, we consider the Riesz mean of the form Dρ(x;sym2f...
Pine-oak mixed forests in the Qinling Mountains are an essential part of the ecosystem in Northwestern China. Diameter distribution models for four species groups of pine-oak mixed forests were developed using the Weibull function. Both moment and hy...
In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space...
Differentiating between malignant and benign masses using machine learning in the recognition of breast ultrasound (BUS) images is a technique with good accuracy and precision, which helps doctors make a correct diagnosis. The method proposed in this...
The slope stability is a very important problem in geotechnical engineering. This paper presents an approach for slope reliability analysis based on the maximum-entropy method. The key idea is to implement the maximum entropy principle in estimating...
We consider the problem of finding a (non-negative) measure μ on B(Cn) such that ∫Cnzkdμ(z)=sk, ∀k∈K. Here, K is an arbitrary finite subset of Z+n, which contains (0,…,0), and sk are prescribed complex numbers (we use the...
A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Importa...
The principal objective of this article is to develop new formulas of the so-called Chebyshev polynomials of the fifth-kind. Some fundamental properties and relations concerned with these polynomials are proposed. New moments formulas of these polyno...
In this paper, we provide a new bivariate distribution obtained from a Kibble-type bivariate gamma distribution. The stochastic representation was obtained by the sum of a Kibble-type bivariate random vector and a bivariate random vector builded by t...
In order to represent the data with non-monotonic failure rates and produce a better fit, a novel distribution is created in this study using the alpha power family of distributions. This distribution is called the alpha-power Kum-modified size-biase...
Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasing...
The maximum entropy method is a theoretically sound approach to construct an analytical form for the probability density function (pdf) given a sample of random events. In practice, numerical methods employed to determine the appropriate Lagrange mul...
To examine the effects of weak intermolecular interactions on solid-phase extraction (SPE) and chromatographic separation, we synthesized some novel stationary phases with a heavy atom effect layer by immobilizing halogenated aromatic rings and hydro...
This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new f...
The paper investigates the problem of performing a correlation analysis when the number of observations is large. In such a case, it is often necessary to combine random observations to achieve dimensionality reduction of the problem. A novel class o...
The method for the prediction of extreme vertical wave bending moments on a passenger ship based on the hindcast database along the shipping route is presented. Operability analysis is performed to identify sea states when the ship is not able to nor...
In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function bui...
In this article, a new four-parameter lifetime model called the exponentiated generalized inverted Gompertz distribution is studied and proposed. The newly proposed distribution is able to model the lifetimes with upside-down bathtub-shaped hazard ra...
This paper is set to analytically describe properties of the hyperbolic distribution. This law, along with the variance-gamma distribution, is one of the most popular normal mean–variance mixtures from the point of view of various applications....
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