Recurrence Relations for Moments of Dual Generalized Order Statistics from Weibull Gamma Distribution and Its Characterizations

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records.We present characterizations ofWGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazrad function

Wave propagation over a beach within a nonlinear theory

Wave propagation over a beach is considered within a nonlinear theory in shallow water. Lagrangian coordinates are used to describe the problem. The solution is expanded in double series involving a small parameter and local oscillations. Two cases are treated: The beach with appreciable inclination on the horizontal (cliff) and the beach of small inclination. We show that finite solutions are obtained, in contrast to the linear theory which involves a logarithmic singularity at the shoreline. For the cliff, it is shown that local oscillations do not appear in the first two orders of approximation, and the incident wave is totally reflected without loss of energy at this order of approximation. The case of an incident wave on the beach is considered. The deformation of this wave is investigated and explicit formulae are obtained for the reflected wave and for the local oscillations, to shed light on the energy transfer due to interaction with the beach

Reliability and Cost-Benefit Efficient in a Two-Dissimilar- Unit with Warm Unit Standby Case Subject to Arbitrary Repair and Replacement

In this paper, we deal with a warm case of standby system made up of two-dissimilar-units. One of these units is a high quality unit, while the other is a low quality one and may require repairs or replacement with a different lesser device in the event of failure, so the first unit is given priority in use. Assume that an arbitrary distribution for repairing the main unit and standby unit. We also examine all transition probabilities and calculate mean sojourn time, availability, and repair time. In the end, we use all of the previous measurments to evaluate the cost-benefit of the system

Power Rayleigh Distribution for Fitting Total Deaths of Covid-19 in Egypt

The Rayleigh distribution incorporate the lifetime of an object or a service time. In this paper, a new model, called, Power Rayleigh distribution (PR) is submitted for specifying the confirmed total deaths of Corona virus (Covid-19) in Egypt. Statistical and reliability properties of the PR distribution such as survival function, failure rate function, mean residual life, order statistic and extreme value distribution are deduced and studied. Maximum likelihood method is used to evaluate the unknown parameters. Simulation Schemes are introduced. Finally, two sets of real-life data are construed and observed that the new model can provide a best fit to water runoff data and the total deaths of Covid-19 data than other well-known distributions

An Ensemble of Optimal Trees for Classification and Regression (OTE)

Predictive performance of a random forest ensemble is highly associated with the strength of individual trees and their diversity. Ensemble of a small number of accurate and diverse trees, if prediction accuracy is not compromised, will also reduce computational burden. We investigate the idea of integrating trees that are accurate and diverse. For this purpose, we utilize out-of-bag observation as validation sample from the training bootstrap samples to choose the best trees based on their individual performance and then assess these trees for diversity using Brier score. Starting from the first best tree, a tree is selected for the final ensemble if its addition to the forest reduces error of the trees that have already been added. A total of 35 bench mark problems on classification and regression are used to assess the performance of the proposed method and compare it with kNN, tree, random forest, node harvest and support vector machine. We compute unexplained variances and classification error rates for all the methods on the corresponding data sets. Our experiments reveal that the size of the ensemble is reduced significantly and better results are obtained in most of the cases. For further verification, a simulation study is also given where four tree style scenarios are considered to generate data sets with several structures

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Clay-based bricks' rich illite mineral for gamma-ray shielding applications: An experimental evaluation of the effect of pressure rates on gamma-ray attenuation parameters

The objective of this study is to increase the natural clay mineral-based bricks' ability to shield γ-rays without the use of external doping materials. Six brick samples were consequently developed at various pressure rates (PRs). The chemical composition and structure of the manufactured bricks are unaffected by the PR applied. The main constituents in the clay used to make bricks are illite and quartz minerals, according to an X-ray diffraction pattern. Additionally, scanning electron microscopy and energy dispersion X-rays have demonstrated the morphology and chemical composition of the used clay. Besides, the Mh-300A density meter shows an increase in the fabricated bricks' density by increasing the PR, where the brick's density increased by 32.92% by increasing the PR from 7.61 to 114.22 MPa, respectively. Also, the effects of the PR on the radiation shielding properties of the fabricated bricks were investigated using a NaI (Tl) detector. The data reveal that increasing the PR between 7.61 and 114.22 MPa improved the linear attenuation coefficient by 44.5, 23.8, 24.2, and 24.8%, respectively, for gamma-ray energies of 0.662, 1.173, 1.252, and 1.332 MeV. The capacity of fabricated bricks to shield against radiation increases as the linear attenuation coefficient increases. The lead's equivalent thickness and half-value thickness of the fabricated clay-based bricks, on the other hand, decreased. As a result, the compacted natural clay brick, which is a lead-free material, provides a suitable alternative for gamma-ray shielding in radioactive locations. © 2023 the author(s), published by De Gruyter.IFP-IMSIU-2023005Funding information: The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research through project number IFP-IMSIU-2023005. The authors also appreciate the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) for supporting and supervising this project

Amenability of heap leaching technology on uranium extraction from Gattar and El Missikat area, Eastern Desert, Egypt: A kinetic approach

Studies of uranium heap leaching from different uranium mineralization situated in Eastern Desert of Egypt was investigated via batch experiments, followed by its optimum condition applicationon column percolationtests.The optimum process operating parameters were implemented on large column scale in order to make more condition control and evaluate the time and reagents needed in the large scale. The results show thatleaching efficiency of GIIattained about 78.3% with 34kg/ton acid consumption in a 44 days period, while leaching efficiency of El-Missikat attained about 86.6% with 28kg/ton acid consumption in a 40 days period.Kinetics reaction models of column tests have been investigated to optimize the column leaching behavior. Based on the leaching results of two mineralized samples, the rate of the uranium metal dissolution is controlled by the chemical reaction and the diffusion reaction but diffusion reaction control was more predominate than a chemical reaction control