Outlier detection consists in detecting anomalous observations. Recently, outlier detection methods have proposed to mine all frequent patterns in order to compute the outlier factor of each transaction. This paper provides exact and approximate methods for calculating the frequent pattern outlier factor without exhaustive enumeration. We propose an algorithm that returns the exact FPOF without mining any pattern. We also present an approximate method where the user controls the maximum error on the estimated FPOF. A study shows the interest of both methods for large datasets where exhaustive mining fails to provide the exact solution. The accuracy of our approximate method outperforms the baseline approach.