In this paper, a new four parameter zero truncated Poisson Frechet distribution is
dened and studied. Various structural mathematical properties of the proposed model
including ordinary moments, incomplete moments, generating functions, order statistics,
residual and reversed residual life functions are investigated. The maximum likelihood
method is used to estimate the model parameters. We assess the performance of the max-
imum likelihood method by means of a numerical simulation study. The new distribution
is applied for modeling two real data sets to illustrate empirically its
exibility.