Diagnosis of paternity for cases without mother and without both mother and putative father based on blood group findings from the relatives

Summary Formulas of the estimated likelihood ratio Y/X are derived for cases without mother as well as those without both mother and putative father, by using blood group findings of their relatives.The distribution curves of the relative frequencies of log(Y/X) for these cases are calculated with respect to 10⁴ families which are created by a Monte Carlo simulation. The extent of success in the paternity diagnosis is clarified by the statistical analysis based on these distribution curves.According to the above analysis, fairly high chance of success can be obtained in the diagnosis of such ambiguous cases without the plaintive mother and/or the putative father, if their relatives are alive. It is also concluded that the genetic information as to the parents of the deceased person increases the exclusion probability, whereas that as to the spouse and children increases the fraction of log(Y/X) > 1 for non-father, corresponding to the fraction where the Essen-Möller value is less than 9%.