In addition to their common use for private online communication, anonymous communication networks can also be used to circumvent censorship. However, it is difficult to determine the extent to which they are actually used for this purpose without violating the privacy of the networks' users. Knowing this extent can be useful to designers and researchers who would like to improve the performance and privacy properties of the network. To address this issue, we propose a statistical data collection system, PrivEx, for collecting egress traffic statistics from anonymous communication networks in a secure and privacy-preserving manner. Our solution is based on distributed differential privacy and secure multiparty computation; it preserves the security and privacy properties of anonymous communication networks, even in the face of adversaries that can compromise data collection nodes or coerce operators to reveal cryptographic secrets and keys. Copyright is held by the owner/author(s)