Asymptotic properties of maximum likelihood estimates for a bivariate exponential distribution and mixed censored data

Di Chen, Jye Chyi Lu, Jacqueline M. Hughes-Oliver, Chin-Shang Li

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This article investigates asymptotic properties of the maximum likelihood estimators (MLE) of parameters in the bivariate exponential distribution (BVE) of Marshall and Olkin (1967) based on the following mixed censored data. In life-testing two-component parallel systems (A, B), a cost-saving procedure is to stop the testing experiment after observing the first r failure times of component A. The resulting data are (X(1), Y*[1]), (X(2), Y*[2]), . . . , (X(r), Y*[r]), (X*(r+1), Y*[r+1]), . . . , (X*(n) Y*[n]), where X(1) ≤ X(2) ≤ ⋯ ≤ X(r) are ordered lifetimes from component A, and Y[i] is the concomitant order statistic corresponding to X(i) from component B. The data X*(r+1), . . . , X*(n), and Y*[i], i = 1, . . . , n are all censored at time X(r) = x(r). Because of the complexity of the data type and the irregularity of the BVE distribution of (X, Y), there are no immediately applicable asymptotic results for the MLE. This article provides a rigorous treatment of the asymptotic behavior of the MLE, with a numerical example illustrating the mathematical derivations.

Original languageEnglish (US)
Pages (from-to)109-125
Number of pages17
JournalMetrika
Volume48
Issue number2
StatePublished - 1998
Externally publishedYes

Fingerprint

Bivariate Exponential Distribution
Mixed Data
Censored Data
Maximum Likelihood Estimate
Asymptotic Properties
Maximum Likelihood Estimator
Life Testing
Failure Time
Irregularity
Parallel Systems
Order Statistics
Immediately
Lifetime
Asymptotic Behavior
Numerical Examples
Testing
Censored data
Maximum likelihood
Asymptotic properties
Exponential distribution

Keywords

  • Asymptotic theory
  • Concomitants of order statistics
  • Life-testing
  • Marshall-Olkin distribution
  • Maximum likelihood estimation

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Asymptotic properties of maximum likelihood estimates for a bivariate exponential distribution and mixed censored data. / Chen, Di; Lu, Jye Chyi; Hughes-Oliver, Jacqueline M.; Li, Chin-Shang.

In: Metrika, Vol. 48, No. 2, 1998, p. 109-125.

Research output: Contribution to journalArticle

Chen, Di ; Lu, Jye Chyi ; Hughes-Oliver, Jacqueline M. ; Li, Chin-Shang. / Asymptotic properties of maximum likelihood estimates for a bivariate exponential distribution and mixed censored data. In: Metrika. 1998 ; Vol. 48, No. 2. pp. 109-125.
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