International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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An Intuitionistic Fuzzy Approach to Solve Multi-objective Transportation Problem

Manmath Haridasrao Lohgaonkar , Vijay Narkhede

Shri Chhatrapati Shivaji College Shrigonda, India

Joint Director, Higher Education Pune, India

ABSTRACT

The aim of this paper is to develop a new concept of optimization technique using Atanassov’s intuitionistic fuzzy sets (IFS), to solve multi-objective transportation problem. It refers to a special class of vector minimum linear programing problem in which the constraints are of equality type and all the objectives are conflict with each other. All the methods either generate a set of non-dominated solutions or find a compromise solution. In this paper, we use a special type of linear and non-linear membership functions to solve the multi-objective transportation problem. It gives an optimal compromise solution. In addition, numerical example is also presented to illustrate the methodology.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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A new class of bivariate distributions
including the bivariate normal distribution, with applications

H. M. Barakat , O. M. Khaled , N. Khalil. Rakha

Dept. of Math. Faculty of Sci. Zagazig University, Zagazig, Egypt.

Dept. of Math., Faculty of Sci. Port said University, Port Said, Egypt.

Physics and Engineering Math. Dep., Faculty of Engineering, Port Said University, Port Said, Egypt.

ABSTRACT

In this paper we introduce a new method to add two shape parameters to any baseline bivariate distribution function (df) to get a more felixable generalized family of the bivariate df'. Through the additional parameters we can fully control the type (by controlling the skewness and kurtosis) of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution. The statistical properties of this family is studied. Moreover, we compared this family with some competitors important generalized families of bivariate df's. To motivate the use of the new suggested family, we present a successful example of real data, concerning the air pollution.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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A new extended mixture skew normal distribution,with applications

H. M. Barakat , A. W. Aboutahoun , N. N. El-kadar

Department of Mathematics-Faculty of Science-Zagazig University-Zagazig-Egypt.

Faculty of Science, Alexandria University, Alexandria, Egypt

Current address: Faculty of Science, Alexandria University, Alexandria, Egypt- Permenant address: Department of Statistics Faculty of Science- Benghazi University-Benghazi-Libya

ABSTRACT

The stable symmetric family of distribution functions (df’s) is a family
that contains the reverse of every df belonging to it. It is revealed that this
family is capable of describing many types of statistical data. We show that
the mixture of the skew normal distribution and its reverse, after adding
a location parameter to the skew normal distribution, and adding the same
location parameter with different sign to its reverse, is stable symmetric family
that contains all the possible types of df’s and it has a very remarkable wide
range of the indices of skewness and kurtosis. To motivate the use of the new
suggested family, we present a successful example of real data.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Estimation in Step Partially Accelerated Life Tests for KIW Model Using Progressive Type-II Censoring

In this article, based on progressively type-II censored schemes under step-stress partially accelerated life test model, the maximum likelihood, Bayes, and two parametric bootstrap methods are used for estimating the unknown parameters of the Kumaraswamy inverse Weibull distribution and the acceleration factor. Asymptotic confidence interval estimates of the model parameters and the acceleration factor are also evaluated by using Fisher information matrix. The classical Bayes estimators cannot be obtained in explicit form, so Markov chain Monte Carlo method is used to tackle this problem, which allows us to construct the credible interval of the involved parameters. Finally, analysis of a simulated data set has been also presented for illustrative purposes.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Modeling Correlated Missing Data

Ahmed Mohamed Mohamed El-Sayed

High Institute for Specific Studies Department of Management Information Systems Nazlet Al-Batran, Giza, Egypt.

ABSTRACT

Missing data have occurred in longitudinal studies. Missing data may reduce the
performance of confidence intervals, reduce statistical power and increase the standard
errors. This paper provides a new model for arising the effect of missing data, which are
considered also as correlated binary data, on the correlated binary variables. Depending
on serial dependence, we formulate the model using Markov properties for the correlated
missing data. The alternative quadratic exponential form are employed for the correlated
binary variables. The logit functions are used for modeling the missing data. The
vectorized generalized linear models have used with five cases of correlated missing data
associated with covariates. The simulation study is investigated, using "bindata" and
"VGAM" packages in R program, to indicate the effect of missing data on the regression
model comparing with the model without missing data.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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New Applications to Evaluate the Prediction Intervals with Maple

Prof. A. H. Abd Ellah

Al Baha University, Faculty of Science, Mathematics Department, Al Baha, P.O. Box.(1988), KSA.

ABSTRACT

In these paper we use new applications to evaluate prediction intervals. In this article, we study the problem of predicting future records (two-sample prediction) based on progressive type-II censoring with random removals, were the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds Prediction. Bayesian point prediction under symmetric and symmetric loss functions are discussed. The maximum likelihood (ML) prediction intervals using "plug-in" procedure
for future records are derived. An example is discussed to illustrate the
application of the results under this censoring scheme.

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Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Factors Contributing To Students’ Poor Performance in Mathematics at West African Examination Council (WAEC) and National Examination Council (NECO) in Bauchi State, Nigeria

Hamisu Idi , Adamu Abubakar

Federal Polytechnic Bauchi, Nigeria

Federal Polytechnic Bauchi

ABSTRACT

This paper describes the prevailing academic scenarios of senior secondary schools in Bauchi state with special references to students’ poor performance in mathematics. The research instruments used to collect data was the questionnaire which had both close ended and open ended questions. Correlation and regression analyses were used and analyzed the data. Investigation of prevailing education scenario revealed wide variations of academic environment, managerial statuses of the school (school-based factors), teacher-related factors as well as students' related factors seem to be major factors influencing academic performance as they were found out to be positively correlated with students' poor performance. These include students' negative attitude toward mathematics, fear and anxiety of mathematics, inadequately qualified teachers, poor teaching methods, inadequate teaching materials, and inadequate supervision of teachers by the authority, overcrowded classes were some of the causes of poor performance in mathematics in the study area. The study also revealed that students attributed their failure mainly to lack of material resources, poor teaching methods, bad teacher behavior and poor grounding in the subject at lower levels as well as their fear of the subject. It is anticipated that the findings of this study will give curriculum developers new insights into emerging issues on performance and influence the Ministry of Education on policy formulation. The Ministry of Education should embark on serious in-service training for mathematics teachers, frequent supervision, and inspection by proper authorities.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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The Normal- Generalized Hyperbolic Secant distribution: Properties and Applications

Hazem Al-Mofleh

Tafila Technical University, Tafila 66110, Jordan

ABSTRACT

In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized hyperbolic secant distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Renyi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Sorting Processes : An Analysis with
Different Sampling Strategies

Mahmoud Ragab

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

ABSTRACT

Sorting data is one of the most important problems that play an important rule in many applications in operations research and computer science. Many sorting algorithms are well studied but the problem is not to find a way or algorithm to sort elements, but to find an efficiently way to sort elements. The output is a stream of data in time. We are interested in this flow of data. For the performance of such algorithms, there has been little research on their stochastic behavior and mathematical properties. In this paper we study the mathematical behavior of some different versions sorting algorithms. We also discuss the corresponding running time using
some different strategies.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Fuzzy Inventory Model For Deteriorating Items

HEMANT UMAP

Yashavantrao Chavan Institute of Science, Satara.(M.S.), India.

ABSTRACT

In this paper the total cost and optimum order quantity are obtained in fuzzy sense for deteriorating items and especially considering demand being dependent on selling price and frequency of advertisement. Function principle method is used for defuzzification. Also the median rule is applied to find the optimum Economic Order Quantity [EOQ] and shortage quantity. Solution procedure is illustrated by a numerical example. The sensitivity analysis of the optimum solution with respect to the changes in the different parameter values is also discussed.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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New classes of bivariate distributions
including the bivariate normal distribution, with applications

H. M. Barakat , O. M. Khaled , N. Khalil. Rakha

Dept. of Math. Faculty of Sci. Zagazig University, Zagazig, Egypt.

Dept. of Math., Faculty of Sci. Port said University, Port Said, Egypt.

Physics and Engineering Math. Dep., Faculty of Engineering, Port Said University, Port Said, Egypt.

ABSTRACT

In this paper we introduce a new method to add two shape parameters to any baseline bivariate distribution function (df) to get a more felixable family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's and possesses very wide range of the indices of skewness and kurtosis.
Finally, we compare the families BSSN and FBSSN with some competitors important generalized families of bivariate df's via real data examples.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Reliability Estimation under Type-II Censored Data
from The Generalized Bilal Distribution: comparison
between Bayesian and classical approaches

Ayman M. Abd-Elrahman

Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt.

ABSTRACT

The main object of this article is the estimation of the unknown population
parameters and reliability function for the generalized Bilal model under Type-II
censored data. Both maximum likelihood and Bayesian estimates are considered.
In the Bayesian framework, although we have discussed mainly the squared loss
function, any other loss function can easily be considered. A Gibb’s sampling procedure
is used to draw Markov Chain Monte Carlo (MCMC) samples, which have
been used to compute the Bayes estimates and also to construct their corresponding
credible intervals with the help of two different importance sampling techniques. A
simulation study is carried out to examine the accuracy of the resulting Bayesian estimators
and compare them with the corresponding maximum likelihood estimates.
Application to a real data set is considered for the sake of illustration.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Type II Exponentiated Half Logistic Generated Family of Distributions with Applications

Hazem Al-Mofleh , M. Elgarhy , Ahmed Z. Afify

Tafila Technical University, Tafila 66110, Jordan

Department of Mathematical Statistics, Burraydah colleges, Qassim, KSA. Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Cairo, Egypt.

Department of Statistics, Mathematics and Insurance, Benha University, Egypt.

ABSTRACT

A new family of distributions called type II exponentiated half logistic is introduced and studied. Four new special models are presented. Some mathematical properties of the new family are studied. Explicit expressions for the moments, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Parameter estimation of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Estimating the Modified-Weibull Parameters in Presence of Step-Stress Partially Accelerated Life Testing

Mohamed A. W. Mahmoud , Rashad M. EL-Sagheer , Amr M. Abou-Senna

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

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

Mathematics Department, Faculty of Engineering, Shoubra, Benha University, Cairo, Egypt

ABSTRACT

Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of each item under normal condition follows the modified-Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are considered. The likelihood equations are to be solved numerically to obtain the maximum likelihood estimates. Based on normal approximation to the asymptotic distribution of maximum likelihood estimates, the approximate confidence intervals for the parameters are derived. It is difficult to get explicit form for Bayes estimates, so Markov chain Monte Carlo method is used to solve this problem, which gives us flexibility to construct the credible intervals the for the parameters. Lindley approximation is also being discussed to obtain Bayes estimators. Finally, an illustrative example and simulation studies are being considered.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Concomitants of Order statistics and record values from
FGM Type Bivariate-Generalized Exponential Distribution

H. M. Barakat , E. M. Nigm , M.A. Alawady , I. A. Husseiny

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

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

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

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

ABSTRACT

We introduce the successive iterations in the original FGM type bivariate-generalized
exponential distribution. Some distributional properties of concomitants of order s-
tatistics as well as record values for this family are studied. Recurrence relations
between single as well as product moments of concomitants are obtained.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Asymptotic Distributions of Record Values under Exponential Normalization

H.M.Barakat , E.M.Nigm , E. O. Abo Zaid

Professor of Mathematical Statistics Zagazig University Faculty of Science Mathematics Department

Professor of Mathematical Statistics Zagazig University Faculty of Science Mathematics Department

Assistant Professor -High Institute of Engineering and Technology Zagazig

ABSTRACT

In this article we study the limit distribution of the record values under non-
linear normalization which have called as exponential norming. The corresponding limit laws are called as e-max stable laws. Moreover, we will study the domain of attraction criteria for these types of limit laws.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Alternative analysis of a fluid queue driven by Markovian queue

A.M.K Tarabia , Ali H.El Baz , Abdulaziz M. Darwiesh

Mathematics Department-Faculty of Science-Damietta University-Egypt

Mathematics Department-Faculty of Science-Damietta University-Egypt

Mathematics Department-Faculty of Science-Damietta University-Egypt

ABSTRACT

In this paper, we consider a fluid queue with an infinite buffer capacity which is both filled and depleted by fluid at constant rats. These rats are uniquely determined by the number of customers in an M/M/1/N queue with constants arrival and service rates. An alternative approach to obtain analytical expression for the joint stationary distribution of the buffer level and the state of M/M/1/N queue is given. Through our approach we obtain the determinant of a tridiagonal matrix in terms of the roots of Chebychev's polynomial of second kind. Moreover, we illustrate the effectiveness of the derived formula through graphs and numerical discussion.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Mathematical Statistics.

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Inference on a New Distribution Under Progressive-Stress Accelerated Life Tests Based on Progressively Hybrid Censored Data with Binomial Removals

Saralees Nadarajah , Alaa H. Abdel-Hamid , Atef F. Hashem

aSchool of Mathematics, University of Manchester, Manchester

Faculty of Science, Beni-Suef University

Faculty of Science, Beni-Suef University

ABSTRACT

A new distribution called geometric-Poisson-Rayleigh distribution is proposed based on failures of a parallel-series system. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other six distributions. The progressive-stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the new distribution. It is assumed that its scale parameter satisfies the inverse power law such that the stress is a non-linear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type-I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear-exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed and numerical computations are carried out to compare the performance of the implemented estimation methods