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dc.contributor.authorAhmad F. Al-Khayaten_US
dc.description.abstractThe purpose of this thesis is to introduce the distribution of randomly weighted average (RWA) assuming that the sample size is random. Moreover, the weights of the RWA are random variables from ordered statistics of standard uniform distribution. Functional transformation technique (called Stieltjes transform) and its inversion are applied to acquire the distribution of the RWA. The distribution of the RWA is a function of an independent random variable. Finally, some examples illustrate the usefulness and applicability of innovative application of some known distributionsen_US
dc.publisher Kuwait university - college of graduate studiesen_US
dc.subjectSample : Randomen_US
dc.titleRandomly Weighted Average with Random Sample Sizeen_US
dc.contributor.supervisorProf. Ahmad A. Soltanien_US
dc.description.conclusionsIn this thesis, we describe and show how to find the distribution and properties of the RWA when the sample size, is random. The RWA, is defined as a function of independent random variables and random weights, . The random weights, are defined as the cuts of order statistics having a Uniform distribution over the interval [ ]. The Stieltjes transform method is used to obtain the distribution of . The generalized Stieltjes transform of is expressed in term of the Stieltjes transforms of the distributions of . Then the inversion of the generalized Stieltjes transforms for is applied to find the distribution function of . This technique uniquely specifies the distribution function of . New formulations were derived for the distribution function of under the assumption that the distribution of is Poisson, Geometric, and Negative Binomial. Formulas of the distribution function of are established for each distribution of and applying different distributions of . The distributions of that were assumed in the thesis are Arcsine, Uniform, Wigner, Power Semicircle, and Gamma. Moreover, this thesis established and proved the expected value and the variance of for each selected distribution of Nen_US
dc.contributor.cosupervisorDr. Suja M. Aboukhamseenen_US
Appears in Programs:0480 Statistics & Operations Research
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