  Considering the creation of persistence landscape on a parametrized curve and
structure of sampling, there exists a random process for which a finite mixture
model of persistence landscape (FMMPL) can provide a better description for a
given dataset. In this paper, a nonparametric approach for computing integrated
mean of square error (IMSE) in persistence landscape has been presented. As a
result, FMMPL is more accurate than the another way. Also, the sampling
importance resampling (SIR) has been presented a better description of
important landmark from parametrized curve. The result, provides more accuracy
and less space complexity than the landmarks selected with simple sampling.
