Efficient simulation of complete and censored samples from common bivariate exponential distributions

  • Authors:

  • Qinying He;H. N. Nagaraja;Chunjie Wu

  • Affiliations:

  • Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, China;Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, USA;School of Statistics and Management and the Key Laboratory of Mathematical Economics Ministry of Education, Shanghai University of Finance and Economics, Shanghai, China

  • Venue:
  • Computational Statistics
  • Year:
  • 2013

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Abstract

Let $$(X_{i:n},Y_{[i:n]})$$ be the vector of the $$i$$ th $$X$$ -order statistic and its concomitant observed in a random sample of size $$n$$ where the marginal distribution of $$X$$ is absolutely continuous. We describe some general algorithms for simulation of complete and Type II censored samples $$\{(X_{i:n}, Y_{[i:n]}), 1 \le i \le r \le n\}$$ from such bivariate distributions. We study in detail several algorithms for simulating complete and censored samples from Downton, Marshall---Olkin, Gumbel (Type I) and Farlie-Gumbel-Morgenstern bivariate exponential distributions. We show that the conditioning method in conjunction with an efficient simulation of exponential order statistics that exploits the independence of spacings provides the best method with substantial savings over the basic method. Efficient simulation is essential for investigating the finite-sample distributional properties of functions of order statistics and their concomitants.