Abstract: Yule-Simon distribution has a wide range of practical applications, such as in network science,biology and humanities. A lot of work focus on the study of how well the empirical data fit YuleSimon distribution or how to estimate the parameter. There are still some open problems such as the error analysis of parameter estimation, the theoretical proof of the convergence of the iterative algorithm for parameter maximum likelihood estimation. The Yule-Simon distribution is a heavy-tailed distribution and the parameter is usually less than 2, so the variance does not exist. This makes it difficult to give an interval estimation of the parameter. Using the compression transformation, this paper gives a method of interval estimation based on the central limit theorem.The other two asymptotic confidence intervals of the parameter are obtained based on the maximum likelihood method and the mode method. These estimation methods are compared by simulations and applications in an empirical data.