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

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  • Qinying He
  • H. Nagaraja
  • Chunjie Wu

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Qinying He & H. Nagaraja & Chunjie Wu, 2013. "Efficient simulation of complete and censored samples from common bivariate exponential distributions," Computational Statistics, Springer, vol. 28(6), pages 2479-2494, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2479-2494
    DOI: 10.1007/s00180-013-0415-8
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    References listed on IDEAS

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    1. Yu, Yaming, 2008. "Efficient simulation of a bivariate exponential conditionals distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2273-2276, January.
    2. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
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    Cited by:

    1. Yusuf Can Sevil & Tugba Ozkal Yildiz, 2022. "Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling," Computational Statistics, Springer, vol. 37(4), pages 1695-1726, September.
    2. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2017. "Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 151-174, March.

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