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We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with…
In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized…
We give a recursive definition of generalized parking function that allows us to view them as a species. From there we compute a non-commutative characteristic of the generalized parking function module, and deduce some enumeration formulas…
The logarithm function and the exponential function are, by nature, base dependent. Thus, in this paper I introduces an arbitrary base in the logarithm and exponential functions, both dependent on $q$, in order to have $\log_a(x;q)$ and…
We consider a particular generalized Lambert function, $y(x)$, defined by the implicit equation $y^\beta = 1 - e^{-xy}$, with $x>0$ and $ \beta > 1$. Solutions to this equation can be found in terms of a certain continued exponential.…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both…
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…