‎Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day‎. ‎In this paper‎,  ‎we introduce a modified symmetric version of the classical Laplace distribution‎.  ‎We provide a comprehensive theoretical description of this distribution‎. ‎In particular‎, ‎we derive the formulas for th...

where {ξ(k, j) : k, j = 1, 2, · · · } and {η(k) : k = 1, 2, · · · } are two independent families of i.i.d. random variables taking values in N := {0, 1, 2, · · · }. The distribution of ξ(k, j) is called the offspring distribution and the distribution of η(k) is called the immigration distribution. Let g(·) and h(·) be the generating functions of ξ(k, j) and η(k), respectively. It is easy to see...

In this study, the thermal characteristics of turbulent nanofluid flow in a helical tube in the tube heat exchanger (HTTHE) were assessed numerically through computational fluid dynamics (CFD) simulation. The findings of both the turbulent models: realizable k-epsion (k-ε) and re-normalisation group (RNG) k-epsilon were compared. The temperature distribution contours show that realizable and RN...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎  [-1,1] to [-1,k]‎‎. ‎At this point‎, ‎the generated distributions gain more&lrm...

A discrete distribution p, over [n], is a k-histogram if its probability distribution function can be represented as a piece-wise constant function with k pieces. Such a function is represented by a list of k intervals and k corresponding values. We consider the following problem: given a collection of samples from a distribution p, find a k-histogram that (approximately) minimizes the `2 dista...

The iron-based catalyst was prepared by a microemulsion method. The composition of the final nanosized iron catalyst, in terms of the atomic ratio, contains 100Fe/4Cu/2K. The experimental techniques of XRD, BET, TEM, and TPR were used to study the phase, structure, and morphology of the catalyst. Fischer-Tropsch synthesis (FTS) reaction test was performed in a fixed bed reactor under pressure o...