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Mathematical Sciences Letters
An International Journal



A study on Beta Exponential-Generalized Inverted Exponential Distribution

Abd El-moneim A.M. Teamah,
Abstract :
We conclude a new distribution titled the beta exponential-generalized inverted exponential distribution. Also, we debate the density, survival, and hazard functions of this distribution. And, discuss some characterization of the double truncated beta generalized inverted exponential (DTBGIE) distribution such: the mean deviation, mode, moments, quantiles, and entropies. Furthermore, the parameters of this model are estimated using the maximum likelihood method (MLE). Additionally, we use the simulation of Monte Carlo to evaluate the performance of estimating the parameters. Finally, We’re applying this model to a real set of data.


Alpha Power Modified Weibull Distribution: Actuarial Measures and Applications to Failure Data

Irene Dekomwine Angbing, Abdul Ghaniyyu Abubakari, Suleman Nasiru,
Abstract :
In this study, a new modified Weibull distribution, called the alpha power modified Weibull distribution, is proposed and studied. The new distribution is a generalization of several well known distributions. The shapes of the density and hazard rate functions are obtained. The density function indicates several shapes including skewed, approximately symmetric and decreasing shapes. The hazard rate function also shows shapes including decreasing, increasing, bathtub and modified bathtub shapes. Several properties of the distribution including moments, moment generating function, inequality measures, order statistics and stochastic ordering are derived. Also, several actuarial measures are derived. The numerical studies of the actuarial measures of the developed distribution are compared with other distributions. Various estimation methods are used to estimate the parameters of the distribution and a simulation study is conducted to ascertain the performance of the estimators. A bivariate extension of the distribution is also derived in the study. The distribution is used to model two real failure data sets to ascertain its usefulness. The results show that the new distribution can serve as an alternative to modeling failure data sets.


A Bivariate Conditional Frechet Distribution with Application

Hanan Hamdy El-Damray,
Abstract :
In this paper the probability density function of the bivariate conditional Frechet distribution are obtained from conditional and marginal Frechet distribution. Cumulative distribution function, survival function, hazard function and reversed hazard function of the bivariate conditional Frechet distribution are discussed. Also, we determined marginal distribution function, joint moments, marginal moments and covariance matrix for the bivariate conditional Frechet distribution. Estimation the unknown parameters is studied and we applicable bivariate conditional Frechet distribution with the real date.


Transmuted Power Inverse Lindley Distribution Having Applications In Engineering Science

Aijaz Ahmad,
Abstract :
The family of distributions which are derived from baseline distribution drag the attention of researchers from past recent years. In this paper we introduce an extension of power inverse Lindley distribution by using transmutation approach suggested by Shaw and Buckley (2007). Several properties of the explored distribution including moments, moment generating function, reliability analysis and order statistics has been discussed. The behaviour of the probability density function (pdf) and cumulative distribution function (cdf) are shown through graphs. The parameters of the explored distribution are estimated by the familiar method of maximum likelihood estimation. Eventually the usefulness of the explored distribution is illustrated through real life data sets.


Estimation of Chen distribution based on Upper record values

shimaa ashraf abdelsalam mohammed,
Abstract :
According to record values and the associated statistics are interested in many real life applications involving data relating to auction and reverse auction, dynamic purchasing systems and production lines. In this article, we consider the problem of estimating unknown parameters of inverse Chen distribution is obtained based on record values as upper record. We present the maximum likelihood (MLE), Bayes estimators and Lindly approximation method for two parameter of inverse Chen distribution. We have examined Bayes estimates under symmetric loss function based on Monte carlo simulation of record values and numerical Computations. Furthermore the comparisons between the di erent estimators are given.


Global Nonexistence of Solutions for Systems of Quasilinear Hyperbolic Equations with Damping and Source Terms

Yaojun YE,
Abstract :
The initial-boundary value problem for a class of quasilinear hyperbolic equations system in bounded domain is studied. We prove that the solutions with the positive initial energy blow up in finite time under some conditions. The estimates of the lifespan of solutions are given.


Bernoulli Matrix Approach for Solving Two Dimensional Linear Hyperbolic Partial Differential Equations with Constant Coefficients

Abstract :
The purpose of this study is to give a Bernoulli polynomial approximation for the solution of hyperbolic partial differential equations with three variables and constant coefficients. For this purpose, a Bernoulli matrix approach is introduced. This method is based on taking the truncated Bernoulli expansions of the functions in the partial differential equations. After replacing the approximations of functions in the basic equation, we deal with a linear algebraic equation. Hence, the result matrix equation can be solved and the unknown Bernoulli coefficients can be found approximately. The efficiency of the proposed approach is demonstrated with one example.


Unsteady Simulation of Rotor-Stator Interaction in Axial Flow Pump Based on Computational Fluid Dynamics

Zhang Hua, Shi Weidong, Li Tongtong, Yao Jie,
Abstract :
Investigations of the Rotor-Stator Interaction in a axial-flow pump at different conditions are presented in the paper. The numerical simulation of the unsteady flow field is performed with FLUENT codes based on RNG k-ε model and SIMPLEC arithmetic. Numerical results show that the strong-coupling evolutions of static pressure and axial velocity distribution between rotor and stator in multi-conditions are periodic with the rotation of rotor. The interaction of stationary and rotating pressure field leads to periodic flow field distortions and induces pressure fluctuation. It is found that the maximum pressure amplitude of blade passing frequency occurs in the rotor inlet zone, but it deceases very fast backward to the stator. The dominant frequency at monitoring points located at rotor inlet, outlet and stator outlet, corresponds to the blade passage frequency. The axial velocity distortion resulting from the modulation of the interacting stationary and rotating flow field is affected by the blade numbers and thickness of both rotor and stator. The axial velocity shows different distributions at different conditions, and the phase of it changes cyclically.


Anomaly intrusion Detection Based on PLS Feature Extraction and Core Vector Machine

Gan Xu-sheng et al, Gan Xu-sheng et al,
Abstract :
To improve the ability of detecting anomaly intrusions, a combined algorithm is proposed based on Partial Least Square (PLS) feature extraction and Core Vector Machine (CVM) algorithms. Principal elements are firstly extracted from the data set using the feature extraction of PLS algorithm to construct the feature set, and then the anomaly intrusion detection model for the feature set is established by virtue of the speediness superiority of CVM algorithm in processing large-scale sample data. Finally, anomaly intrusion actions are checked and judged using this model. Experiments based on KDD99 data set verify the feasibility and validity of the combined algorithm.


A novel proof of Watsons contour integral representations

Dong-Fang Liu, Xiang-Li Wang,
Abstract :
In this paper we give a simple proof of Watsons contour integral representations for $_{r+1}\phi_{r}$ by applying Cauchys operators, and obtain an interesting formula of contour integral representation for $(q;q)^r_\infty$.

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