8097

7515

كارشناسي ارشد

آمار رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

دوازده،78ص.: نمودار

ص.ع.به فارسي و انگليسي

سروش عليمرادي، سعيد پولادساز، صفيه محمودي

11/8/92

محمد حسن علامت ساز، افشين پرورده

رياضي

ID7515

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Distribution Of Quadratic Forms Under Skew Normal Settings Abstract Many families of density functions approach the normal one as a certain parameter tends to an appropriate value However there are only a few parametric classes of distributions which include the normal one as a proper member and not only as a limit case while in various situations it is useful to deal with a parametric class which allows a continuous variation from normality to non normality It would be ideal to have at hand a class of densities with the following properties i strict inclusion of the normal density ii mathematical tractability iii wide range of the indices of skewness and kurtosis The term skew normal SN refers to a parametric class of probability distributions which written if its density function is includes the standard normal as a special case A random variable Z is said to be skew normal with parameter where and denote the N density and distribution function respectively the which regulates the skewness varies in and corresponds to the parameter N density In past two decades the class of multivariate skew normal distributions has been studied by many authors see e g This class of distributions includes the normal distribution and has some properties like the normal one but is skew In this thesis on the basis Wang at el define a class of skew normal distributions with fewer parameters and which is still settings where the noncentral skew chi square distribution is defined and the properties closed under the linear transformations than On the basis of the multivariate skew normal of quadratic forms are studied in this paper In the last part of this thesis the necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi square distributed random variables are obtained by using their moment generating functions MSC H E Keywords skew normal Multivariate skew normal distribution Noncentral skew chi square distribution quadratic forms generalized noncentral skew chi square PDF created with pdfFactory trial version www pdffactory com

سروش عليمرادي، سعيد پولادساز، صفيه محمودي

محمد حسن علامت ساز، افشين پرورده