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

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

Bayesian estimation of P[Y \u3c X] Based on Record Values from the Lomax Distribution and MCMC Technique

Our interest is in estimating the stress-strength reliability R = P[Y \u3c X], where X and Y follow the Lomax distribution with common scale parameter. We discuss the problem in the situation where the stress measurements and the strength measurements are both in terms of records. Firstly, we obtain the MLE of R in general case (the common scale parameter is unknown). The MLE of the three unknown parameters can be obtained by solving one non-linear equation. We provide a simple fixed point type algorithm to find the MLE. We propose percentile bootstrap confidence intervals of R. A Bayes point estimator of R, and the corresponding credible interval using the MCMC sampling technique have been proposed. Secondly, assuming the common scale parameter is known, the MLE of R is obtained. Using exact distributions of the MLEs of the two unknown parameters, we construct the exact confidence interval of R. In this case, Bayes estimators have been obtained using Lindley\u27s approximations. Analysis of a simulated data set has been presented for illustrative purposes. Finally, the different proposed methods have been compared via Monte Carlo simulation study