Aimed at the problem that α-stable distribution has no closed form expression for the probability density function (PDF)

an approximate expression is suggested.Such model is a mixture of Gaussian and Cauchy with bi-parameter.The mixture ratio is determined by fractional low order moment (FLOM).Proposed model has a complete closed form and provides analytical convenience.Based on such model

this paper further proposes a Rao statistical test method for the detection of sine signal under the α-stable noise environment.We illustrate the detection performances of the proposed Rao test for various α

and compare them with the Rao test that based on Gaussian assumption.Simulation results show that the proposed Rao detector distinctively outperforms the Rao detector that based on Gaussian assumption.