Study of some stable symmetric families of
Distributions

Haroon Barakat

Professor of Mathematical Statistics-Mathematics Department-Faculty of Science-Zagazig University-Egypt

ABSTRACT

Abstract: In this talk we spotlight on the most essential features of the expanded family of distribution functions that best fits any data set. Among these features is the possible types of skewness and kurtosis that the family contains. We call any family that contains all the possible of such types a full family. We suggest a method for constructing a full family, which is based on the additive stable symmetric-normal family (c.f. Barakat, 2015). Moreover, we show that the mixture of any baseline distribution and its reverse, after multiplying and dividing, respectively to them the same scale parameter, is full family. The resulted family has a wide range of the indices of skewness and kurtosis and is capable of fitting a wide spectrum of real world data set.
AMS 2010 Subject Classification: 62-07; 62E10; 62F99.

Inference on a New Lifetime Distribution for a Parallel-Series System under Progressive Type-II Censoring

Alaa H. Abdel-Hamid , Atef F. Hashem

Beni-Suef University

Beni-Suef University

ABSTRACT

A new lifetime distribution with increasing, decreasing or upside-down bathtub shaped hazard rates, called doubly Poisson exponential distribution, is
introduced. One of the motivations of the new distribution is that it may represent the lifetime of units connected in a parallel-series system. Several properties of the new distribution are discussed. Based on progressive type-II censoring, six estimation methods for the involved parameters are considered. The methods are maximum likelihood, moments, least squares, weighted least squares and Bayes (using linear-exponential and general entropy loss functions) estimations. Bayes estimates for the parameters are obtained using Markov chain Monte Carlo algorithm. The performance of these methods is compared through an extensive numerical simulation, based on mean of mean squared errors and mean of relative absolute biases. Two real data sets are used to compare the new distribution with other five distributions. The comparison shows that the former distribution is better to fit the data than the other five distributions

ABSTRACT
This dissertation concerns singularly-perturbed systems of ordinary
differential equations and applications to physical problems with multiple
spatial or temporal scales, such as the FitzHugh-Nagumo, Hodgkin-Huxley and
Gray-Scott equations, predator-prey systems, and excitable membrane systems.
In Part one, a general modular method based on geometric singular
perturbation theory to establish the existence of periodic orbits is
developed. This method exploits the geometry of the systems’ slow manifolds
and their normally hyperbolic structure. It transforms the Poincare map
problem into a boundary-value problem in a naturally-augmented system, and the
periodic orbit is found as the transverse intersection of invariant manifolds.
A modified version of the Exchange Lemma is proven, in which the
transversality of the tracked manifold and the local stable manifold of the
slow manifold is not required.
Independently, a multiple-pulse Melnikov function is constructed for
adiabatic, slowly-varying, Hamiltonian systems. It detects homoclinic orbits
with multiple, successive fast excursions. Combined with the above-mentioned
method, it shows the existence of a wide class of multiple-pulse periodic
orbits in adiabatic systems, such as that modeling resonant sloshing in
shallow water.
In Part two, the focus is on the development of geometric methods to study the
periodic behaviors, mechanisms of frequency control and the functional role of
connectivity in small networks of neurons. Motivated by a subnetwork of the
crustacean stomatogastric ganglion, I study a three-cell network formed by an
intrinsic oscillator, electrically coupled to a bistable element. Both of them
make inhibitory synapses (with different time courses) onto an excitable cell,
which in turn inhibits the bistable element.
By using geometric singular perturbation theory, I find circumstances under
which the electrically coupled pair can effectively be reduced to an intrinsic
oscillator. I also find physiologically plausible conditions under which the
only possible periodic behaviors of the full network are N:1 rhythms, in
which the electrically coupled pair undergoes N oscillations in each
cycle of the excitable element. This is shown by constructing a singular
Poincare map.

Mohammed Abo Elftooh Ghazal , Ahmed Mohamed Metwally Ahmed

Assistant Prof. of Statistics. Mathematics Department, Faculty of Science New Damietta, Damietta University

Scholarship Student in Mathematics Department, Faculty of Science New Damietta, Damietta University

ABSTRACT

Abstract
This paper is devoted to the regression of a stochastic time series on one or more deterministic series. The stochastic series is assumed to be the output of a linear filter with the deterministic series as inputs plus a stochastic error series. The principal goal of the analysis is then to estimate the transfer function of the filter and the spectral structure of the error series and the impulse response function. The data are allowed to be tapered. In this paper expressions are derived for the first- and second-order moments and the asymptotic distributions of estimates of the parameters of interest. From these results we are deduced the asymptotic normality. As an application of the main results in this paper, an example is discussed.

On a Bayesian Classifier based on the Assumption of Generalized Pareto Mixture Modeling

Emtair M. Abdalla

Department of mathematics, Faculty of Science, Sirte university, Libya

ABSTRACT

Traditional parametric classification is based on the assumption that the mixture components are Gaussian of type. The shortcoming of such a classifier is that it is absolutely misleading as much as the assumption is violated. Building a classifier that works for all non-Gaussian parametric assumptions is challenging. In this paper, a classifier based on a typical skewed model that much violates the Gaussian assumption is proposed. The classifier is based on the assumption of generalized Pareto mixture Modeling.

Mathematics Department, Faculty of science, Mansoura University, Mansoura, Egypt.

Department of Mathematies , Faculty of science , Al Azhar University, Cairo, Egypt

Mathematics Department, Faculty of science, Mansoura University, Mansoura, Egypt.

ABSTRACT

Recently the visualization of multi-pivot Quicksort has received the interest of researchers due to Vladimir Yaroslavskiy’s algorithm. The Dual-pivot Quicksort algorithm has been annualized in terms of comparisons and swaps in 2015 by Wild et al. In this paper, we compute the expected number of swaps needed by the Dual-pivot Quicksort to sort an array of distinct n elements.
The main goal is to discuss the convergence ofthe Dual-pivot Quicksort process by utilizing the contraction method. We show that the distribution of the number of swaps done by the duality process converges to a unique fixed point. Consequently when n is large the number of swaps are concentrated around their mean.The idea is a simple expansion of using two pivots by randomly picking k pivots i 1 ,i 2 ,i 3 ,...,i k and partitioning the array simultaneously according to these k pivots.
We extend the result of El-Desouky et al 2015 to obtain the expected number of both comparisons and swaps needed by the 3-pivot Quicksort process to do the job. Using the contraction method, we show
that the distribution of the number of swaps done by 3-pivot Quicksort process converges to a unique fixed point. We generalize the results for Multi-pivot Quicksort. Finaly, in light of these results we establish some relationships between the expected cost of Multi-pivot Quicksort and stirling numbers.

Inference of Progressively Censored Data from The Generalized
Exponential Distribution

N. M. yhiea , M. A. W. Mahmoud , M. Moshref , N. M. Mohamed

Math. Dept., Faculty of Science, Suez Canal Univ., Ismailia.

Math. Dept., Faculty of Science, Al-Azhar Univ., Naser City (1188), Cairo, Egypt

Math. Dept., Faculty of Science, Al-Azhar Univ., Naser City (1188), Cairo, Egypt

Math. Dept., Faculty of Science, Suez Univ., Suez.

ABSTRACT

In this paper, we derive approximate moments of
progressively type-II right censored order statistics from the
generalized exponential distribution . Also, using these moments to
derive the best linear unbiased estimates and maximum likelihood
estimates of the location and scale parameters from the generalized
exponential distribution. In addition, we use Monte-Carlo simulation
method to obtain the mean square error of the best linear unbiased
estimates and maximum likelihood estimates and make comparison
between them. Finally, we will present numerical example to
illustrate the inference procedures developed in this distribution.

Weibull Semiparametric Regression Models under Random Censorship

E. A. Rady , M.M.E. Abd El-Monsef , A.M. Sobhy

ISSR, Cairo University

Mathematic Department, Faculty of Science, Tanta University

Mathematic Department, Faculty of Science, Tanta University

ABSTRACT

Semiparametric regression is concerned with the flexible combination of non-linear functional relationships in regression analyses. The main advantage of the semiparametric regression models is that any application benefits from regression analysis can also benefit from the semiparametric regression. In this paper, we derived a consistent estimator of parametric portion and nonparametric portion in Weibull semi-parametric regression models under random censorship.

The Exponentiated Exponentiated Exponential-Weibull Distribution with application to lifetime data

Ahmed M. T. Abd El-Bar , Shimaa A.Dessoky

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

ABSTRACT

In this paper we introduce a five-parameters distribution called Exponentiated Exponentiated Exponential-Weibull (EEE-W). Its hazard rate function can have different shapes which offers a more flexible model for lifetime data. Several statistical properties of the new probabilistic model are studied. Further, we discuss estimation by the maximum liklehood. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

Some statistical models to forecast the demand situation in the world oil market

Azhari A. Alhag

Mathematics and Staistics Dept., Faculty of Science, Taif university, KSA; International University of Africa, Khartoum,Sudan

ABSTRACT

Forecasting consists basically of using data to predict future value for given
variable to facilitate macro and micro level decision making .There are, of course
many ways to generate prediction ranging in complexity and data requirement .
In this paper we provide statistical analysis for the situation in the world oil market
to understand the relationship between variables using a matrix of correlation
Coefficient, we use the graphical methods and build some statistical models.

Some Problems in Estimation and Prediction with Mathematica

A. H. Abd Ellah

Sohag University, Faculty of Science, Mathematics Department, Soag 82524, Egypt

ABSTRACT

In this paper, we investigate the estimation problem concerning a progressively type-II censored sample from the two-parameter bathtub-shaped lifetime distribution. We use the maximum likelihood method to obtain the point estimators of the parameters.We also provide a method for constructing an exact confidence interval and an exact joint confidence region for the parameters. Two numerical examples are presented to illustrate the method of inference developed here. Finally, Monte Carlo simulation studies are used to assess the performance of our proposed method using Mathematica.

On the Existence and Uniqueness of a Randomized Partial
Quicksort Algorithm

Mahmoud Ragab

Mathematics Department, Faculty of Science, Al Azhar University, Nasr City (11884), Cairo, Egypt.

ABSTRACT

Sorting data is clearly an important problem that play an important rule in many applications in operations research and computer science. Quicksort algorithm invented by Hoare in 1961 is a simple and elegant solution to the sorting problem. Given an input of unsorted n distinct reals, Quicksort sorts them using the divide-and-conquer strategy. on this paper We are focus on the expected running time of the algorithm. We consider the external randomness of the input and specific choice of the pivot. The partial sorting problem is, given an input of reals of size n, sort the l smallest reals out of n. The purpose of this paper is to discuss the behavior of the Quicksort algorithm with external randomness. Using a suitable normalization, the
running time needed by the partial Quicksort to sort l-th smallest out of n seen as a process in l. We present the limiting process nicely as a weighted branching process. In particular, we show the existence of a limiting process with path in the space of cadlag functions.

Robust Variogram Fitting Using Non-Linear Rank-Based Estimators

Hazem M. Al-Mofleh , John E. Daniels , Joseph W. McKean

Department of Mathematic, Tafila Technical University, Tafila, Jordan 66110

Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859 USA

Department of Statistics, Western Michigan University, Kalamazoo, MI 49004 USA

ABSTRACT

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

A Moment inequality to class used better than aged in convex ordering upper tail (UBACT) of life distributions and its applications

S. E. Abu-Youssef , H. E. El-Attar , A. A. El-Toony

Department of Mathematics, Faculty of Science,,l Al- Azhar University, Cairo, Egypt;

Department of Mathematics, Faculty of Science Helwan University, Cairo, Egypt.

Department of Mathematics, Faculty of Science,l Helwan University, Cairo, Egypt.

ABSTRACT

The class of life distributions used better than aged in convex order upper tail ordering
(UBACT) is introduced. A Moment inequality to this class (UBACT) of life distribution is given.
In addition testing exponentiality versus (UBACT) class of life distribution based on a moment
inequality is presented. Simulation such as critical values, Pitman's asymptotic efficiency and
the power of test are discussed. Medical applications are given at the end of the paper.

Department of Statistics, Faculty of Science, University of Bengahzi-Libya. Correspondence to: entesar.el-saeiti@uob.edu.ly

ABSTRACT

This paper discussed the problem of using ordinary least square estimation method to estimate the parameters for correlated data. By neglecting the correlated data autocorrelation problem will Stand out, and logical to expect that the use of ordinary least squares (OLS) for data subject to auto-correlated errors will produce incorrect results and inferences. To solve this problem use “nonparametric Monte Carlo” bootstrapping Time series. The important of bootstrap methods and the modifications needed for their applicability in time series models. The used example is taken from Business Digest (1976), by using OLS estimation method for correlated data. The availability of valid nonparametric “bootstrapping Time series method” inference procedures based on resampling and/or subsampling has freed practitioners from the necessity of resorting to simplifying assumptions such as normality or linearity that may be misleading. This paper explains the problem of using OLS for correlated data and the way to indicate the autocorrelation problem. In addition, it showed the method to discover the autocorrelation problem, and the Optimal Block Length Selection Methods by using R program.

A new generalized Poisson Lomax life time distribution and its application to censored data

Abu-Youssef, S. E , Mohammed, B. I , Sief, M. G

Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt

Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt

Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514

ABSTRACT

We propose a new family of continuous univariate distributions with one extra parameter, the so-called Lomax Poisson (LP) distribution, which have the Lomax distribution as submodel. Various structural properties of the new distribution, including the shape behavior of the density, hazard rate function, moments and mean residual life, are presented. The reliability function $R=P(X>Y) $ and its estimation are discussed. Also, the estimation of the model parameters is given by maximum likelihood. Extensive simulation studies are carried out to investigate the accuracy of the estimates of the model's parameters. Finally, we illustrate the importance of the proposed model by means of fitting to randomly censored data.

Inference for a Step-Stress Partially Accelerated Life Test Model with Progressively Type-II Censored Data from Distributions Having Power Hazard Function

Rashad M. El-Sagheer

Mathematics Department, Faculty of Science, Al-Azhar University, Naser city 11884, Cairo, Egypt.

ABSTRACT

In this article, The maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters of distributions having power hazard function (DPHF) and the acceleration factor as well as some lifetime parameters reliability and hazard functions based on progressively type-II censored schemes under step-stress partially accelerated life test (SSPALT) model. Based on normal approximation to the asymptotic distribution of MLEs, the approximate confidence intervals (ACIs) for the parameters and the acceleration factor are derived. In addition, two bootstrap confidence intervals are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply the Markov chain Monte Carlo (MCMC) technique to compute the Bayes estimates of the parameters and the acceleration factor. Gibbs within the Metropolis Hasting algorithm is applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters have been computed. Finally, analysis of a simulated data set has also been presented to illustrate the proposed estimation methods.

On the Chaotic Dynamics of Stochastic Predator Prey Models

A. Elhassanein

Dept. of Math., Faculty of Science, Damanhour University, Damanhour, Egypt.

ABSTRACT

In this paper, a new forced discrete chaotic predator prey model is presented. The chaotic behavior of the proposed model is investigated. The existence and stability of the equilibria of the skeleton are studied. Numerical simulations are employed to show the model’s complex dynamics by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. Time series diagrams are used to follow the dynamics of the model and discuss the marginal distribution of the state variables. The effects of noise intensity on its dynamics and the intermittency phenomenon are also discussed via simulation.