A-Rahman, A. A., "On Characterizing Oyuang's Family of The second Type Using Lift and Double Truncated Moments", International Journal of Mathematical Archive, vol. 5, issue 9, pp. 210-221, Submitted. AbstractWebsite

This paper considers characterizations of a certain class of probability distributions proposed by Oyuang [20]. A recurrence relation between two consecutive conditional moments of h(Z) given x

A.A-Rahman, A., "Characterizations of a Mixture of Two Exponential Families", Applied Mathematical Sciences, vol. 7, issue 78, pp. 3861-3872, 2013. Abstractabstract_mixture_of_two_exo_families.docx

A mixture from two exponential families is identified using a differential equation, a recurrence relation between conditional moments and conditional variance. New characterizations to other different mixtures are deduced. Some well-known results follow as special cases from our results.

A-Rahman., A. A., "On Characterizing Some Mixtures of Probability Distributions.", Juornal of Applied Mathematics and Bioinformatics., vol. 3, issue 3, pp. 153-172, 2013. Abstract

The concept of recurrence relations is used to characterize mixtures of two exponential families, two 1st type Ouyang's distributions and two 2nd type Ouyang's distributions. Our results are used to deduce conclusions concerning some mixtures of some well known distributions like Burr, Pareto, Power Weibull, 1sttype Pearsonian and Ferguson's distributions. Furthermore, some characterizations related to some recently distributions like, mixtures of two exponentiated Weibull, exponentiated Pareto and generalized exponential distributions are derived from our results. In addition, some well-known results follow from our results as special cases.

A-Rahman., A. A., "A Unified Approach of Some Characterization Results", Journal of Statistics and Mathematics. Bioinfo. Publications. , vol. 4, issue 1, pp. 141-146, 2013. Abstract

This paper considers the problem of identifying some probability distributions using the concepts of right and left truncated moments of some function of the kth order statistic. Furthermore, it investigates the necessary and sufficient conditions to characterize distributions by the equation as well as Some wellknown results follow from our results as special cases.

A.A-Rahman., A., "On Characterization of a Certain Family of Distrbutions Based on Some Recurrence Relations", Int. J. Contemp. Math.Sciences, vol. 7, issue 44, pp. 2167-2177, 2012. Abstracton_characterization_of_certatin_family_of_distributions.pdfsome_characteristic_properties_of_the_exponential_family.pdf

In this paper, three recurrence relations for a certain class of probability
distributions are presented. The first one is a recurrence relation between conditional
moments of h(X) given X > y. The second is the relationship between the moments
E( ( )), E( ( )) and E( ( )), where is the order statistic from a sample
of size n. The last one is the relationship between the conditional moments E( ( )| >t)
and E( ( )| >t). Some results concerning Modified Weibull, Weibull, Rayleigh,
exponential, Linear failure rate, 1 type Pearsonian distributions, Burr, Pareto power and
uniform distributions are obtained as special cases.

Rahman, A. A. A., "A Unified Approach for Mixtures from Two Certain Families of Distributions", Applied Mathematical Sciences, vol. 7, issue 29, pp. 1419 - 1428, 2013. Abstract

A mixture from two distribution families is characterized via a differential equation as well as a recurrence relation between three consecutive conditional moments of some function ( ), k = 1, 2, 3 ... given X > y. Some wellknown results follow as special cases from our results.

A.A-Rahman., A., "Some Characteristic Properties Of The Exponential Family", Journal of Statistics and Mathematics, vol. 3, issue 3, pp. 130-133, 2012. Abstractsome_characteristic_properties_of_the_exponential_family.pdf

In this paper, two recurrence relations characterizing a certain class of distribution family are presented. The first one is a recurrence relation between conditional moments of ℎ(X) given X < y. The second is a relationship between the conditional momentsn and where Yk is the kth order statistic from a sample of size n. Finally the concept of conditional variance of ℎ(Yk) given Yk > t is used to characterize this family. Some results concerning Modified Weibull, Weibull, Rayleigh, exponential, Linear failure rate, 1st type Pearsonian distributions, Burr, Pareto, Power and uniform distributions are obtained as special cases. Keywords- Characterization, truncated moments, conditional variance, order statistics, recurrence relations, Modified Weibull, Linear failure rate, Pearson distribution of the first type, Burr, and Power distributions.

A.A-Rahman., A., "Identifying A Certain Class Of Distributions Using Some Recurrence Relations", International Journal of Mathematical Archive, vol. 3, issue 8, pp. 2997-3003, 2012. Abstractmathematical_archieve_research8.pdfWebsite

In this paper, three recurrence relations for a certain class of probability distributions are presented. The first one is a recurrence relation between conditional moments of h(X) given X < y. The second is the relationship between the moments E(h^m(Y_(k+1))), E(h^m(Y_k)) and E(h^(m-1)(Y_k)), where Y_k is the k^th order statistic from a sample of size n. The last one is the relationship between the conditional moments E(h^m(Y_k)|Y_k

Dr. Ali Abdel Rahman, Associate Professor Of Mathematical Statistics Field Of Interest: Characterizations +Discrete Mathematics

Dr. Ali Abdel Rahman, Associate Professor Of Mathematical Statistics

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