Abstract: A mixed point process decomposition based on k-th nearest distance is introduced.Disadvantage in former researches is revealed and resovled.It is shown that the threshold of applicability judgment is not influenced as R is larger or smaller than critical value.Primary influences show as R is close to the theoretical calculation.Difference between theoretical and calculated R is analyzed. And numerical experiment is done.It is noticed that whether the critical value is revised or not,it depends on the number of point with almost a negative eorrelativity.In other words,the critical value is higher as sample size is small but is lower as sample size is large. As R lies in critical conditions.the inifialized valid value of k increases with increasing of sample size.

Key words: clusters, k-th nearest-neighbour, ratio of density, rectification