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Background & Aim: In the survival data with Long-term survivors the event has not occurred for all the patients despite long-term follow-up, so the survival time for a certain percent is censored at the  end  of the  study.  Mixture  cure  model  was  introduced  by Boag,  1949  for  reaching  a  more efficient analysis of this set of data. Because of some disadvantages of this model non-mixture cure model was introduced by Chen, 1999, which became well-known promotion time cure model. This model was based on the latent variable distribution  of N. Non mixture cure models has obtained much  attention  after the introduction  of the latent activating  Scheme  of Cooner,  2007, in recent decades, and diverse distributions have been introduced for latent variable. Methods  & Materials:  In this article,  generalized  Poisson- inverse  Gaussian  distribution  (GPIG) will be presented for the latent variable of N, and the novel model which is obtained will be utilized in analyzing long-term survival data caused by skin cancer. To estimate the model parameters with Bayesian  approach,  numerical  methods  of  Monte  Carlo  Markov  chain  will  be  applied.  The comparison drawn between the models is on the basis of deviance information criteria (DIC). The model with the least DIC will be selected as the best model. Results: The introduced  model  with GPIG, with deviation  criterion  of 411.775, had best fitness than  Poisson  and  Poisson-inverse  Gaussian  distribution  with  deviation  criterion  of 426.243  and 414.673, respectively. Conclusion: In the analyzing long-term survivors, to overcome high skewness and over dispersion using distributions that consist of parameters to estimate these statistics may improve the fitness of model. Using distributions which are converted to simpler distributions in special occasions, can be applied as a criterion for comparing other models.