In article <[EMAIL PROTECTED]>, Douglas C. <[EMAIL PROTECTED]> wrote: >Suppose a rv has support only on R+ (i.e. a non-negative rv). Given >integer moments of x, m1, m2,...mn, how might I compute bounds on some >_other_ moment m_n+1?
>For instance, suppose I fix the first and second moment. What are the >bounds on the third moment? >If this is fully covered in some text, I'd appreciate a reference. This is fully covered in Shohat and Tamarkin, and probably in any other book on the moment problem. The conditions are that the expected value of a non-negative polynomial (or function, if other than consecutive powers are used) is non-negative. For the n+1 moment on R+, this means that the appropriate one of the matrices with a_ij = m_i+i or b_ij = m_i+j+1, i, j starting at 0, with m_n+1 the last element, is positive semi-definite, assuming no previous one is singular. One singular matrix determines the distribution exactly. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
