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On Approximating the Distribution of Indefinite Quadratic Forms by Moments Approach
Ghasem Rekabdar , Rahim Chinipardaz , Behzad Mansouri
Abstract:   (477 Views)
‎In this study‎, ‎the multi-parameter exponential family of distribution has been used to approximate the distribution of indefinite quadratic forms in normal random vectors‎. ‎Moments of quadratic forms can be obtained in any orders in terms of representation of the quadratic forms as weighted sum of non-central chi-square random variables‎. ‎By Stein's identity in exponential family‎, ‎we estimated parameters of probability density function‎. ‎The method handled in some examples and we indicated this method suitable for approximating the quadratic form distribution.
Keywords: ‎Quadratic form‎, ‎Multivariate Normal Distribution‎, ‎Non-Central Chi-Square Distribution‎, ‎Durbin-Watson Statistic‎.
Full-Text [PDF 4472 kb]   (83 Downloads)    
Type of Study: Applied | Subject: General
Received: 2015/07/16 | Accepted: 2018/10/11
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مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences
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