ISSN: 2250-3005 - ijcer

INTERNATIONAL JOURNAL OF COMPUTATIONAL ENGINEERING RESEARCH (IJCERONLINE.COM) VOL. 2 ISSUE. 8Statistical Distributions involving Meijer’s G-Function of matrixArgument in the complex case1, Ms. Samta 2, Prof. (Dr.) Harish Singh1 Research Scholar, NIMS University2 Professor Department of Business Administration, Maharaja Surajmal Institute,Guru Gobind Singh Indraprastha University, DelhiAbstract:The aim of this paper is to investigate the probability distributions involving Meijer’s g Functions of matrixargument in the complex case. Many known or new Result of probability distributions have been discussed. All thematrices used here either symmetric positive definite or hermit ions positive definite.IIntroduction: The G-FunctionThe G-functions as an inverse matrix transform in the following form given by Saxena and Mathai (1971).1.1For p < q or p = q, q ≥ 1, z is a complex matrix andthe gamma products are such thatthe poles of and those of are separated.II.The DistributionIn the multivariate Laplace type integraltakingThe integral reduces toFor and is hermitian positive definite matrix and is an arbitrarycomplex symmetric m X m matrix.The result (2.1) is a direct consequence of the result Mathai and Saxena (1971, 1978).[Notationfor exponential to the powerThus the function2.1whereelse whereprovides a probability density function (p.d.f)2.1 Special CasesCase (i)Replacing letting tends to null matrix and using the result due to Mathai (1977)Issn 2250-3005(online) December| 2012 Page 101