The problem of a background in the nuclide activities 
estimation by the maximum likelihood method

S.A. Tolstov

      A problem  of  the nuclides activities estimation by the maximum
likelihood  method  has  been  investigated  for  the   case   of   an
experimentally   measured   background.   It   was   assumed  that  an
investigated spectrum has a Poisson distribution in  channels,  shapes
of  all  spectral  components are known except a background component.
Therefore,  two  spectra  should  be  measured  to   obtain   nuclides
activities estimates:  spectrum of investigated sample and spectrum of
a background.
      The set   of   the  non-linear  equations  has  been  found  for
calculation of  the  maximum  likelihood  estimates  of  the  nuclides
activities.  The  fast iteration algorithm has been developed to solve
the obtained set of the non-linear equations.