The problem of uncertainty claim pricing using distortion operators is considered in this research paper. This approach was first developed in insurance pricing, where the original distortion function was defined in terms of the normal probability distribution. This approach is generalized by using a distortion that is based on the Weibull distribution in this research paper. The Weibull family allows for heavier and skewed tail because it is so flexible that other statistical distributions can be recovered from it by change of parameters. The problem of uncertainty claims has been extensively studied for non-Gaussian model in which the formula was derived for the normal Inverse Gaussian distribution Asset pricing. It is shown in this paper how Weibull based distortion function can used to derive the formula for asset pricing of uncertainty future returns of a risky asset. The risk measure for the incurred risk modelled by the Weibull variables was derived and it was shown that it follows the power law.