This paper discusses the estimation of R = P (Y <; X) when X and Y are independent generalized exponential random variables with different scale parameters and the same shape parameter based on progressive type-II censoring samples. The maximum likelihood estimator (MLE) of the parameter R is obtained. The approximate MLE (AMLE) of R by the Taylor series expansion is proposed. The asymptotic distribution of R is derived to construct the asymptotic MLE and AMLE confidence intervals. Also, the bootstrap-p and bootstrap-t confidence intervals are constructed. In addition, using the Metropolis-Hasting procedure, we derive the Bayes estimate and the corresponding credible interval. Finally, a Monte Carlo simulation and an analysis of two real datasets are presented to evaluate the various proposed methods.

Computing two-way and multi-way set similarities is a fundamental problem. This study focuses on estimating 3-way resemblance (Jaccard similarity) using b-bit minwise hashing. While traditional minwise hashing methods store each hashed value using 64 bits, b-bit minwise hashing only stores the lowest b bits (where b>= 2 for 3-way). The extension to 3-way similarity from the prior work on 2-way similarity is technically non-trivial. We develop the precise estimator which is accurate and very complicated; and we recommend a much simplified estimator suitable for sparse data. Our analysis shows that $b$-bit minwise hashing can normally achieve a 10 to 25-fold improvement in the storage space required for a given estimator accuracy of the 3-way resemblance.