Parameter estimation for bivariate shock models with singular distribution for censored data with concomitant order statistics

Di Chen, Chin-Shang Li, Jye Chyi Lu, Jinho Park

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

When two-component parallel systems are tested, the data consist of Type-II censored data X(i), i = 1, . . . , n, from one component, and their concomitants Y[i] randomly censored at X(r), the stopping time of the experiment. Marshall & Olkin's (1967) bivariate exponential distribution is used to illustrate statistical inference procedures developed for this data type. Although this data type is motivated practically, the likelihood is complicated, and maximum likelihood estimation is difficult, especially in the case where the parameter space is a non-open set. An iterative algorithm is proposed for finding maximum likelihood estimates. This article derives several properties of the maximum likelihood estimator (MLE) including existence, uniqueness, strong consistency and asymptotic distribution. It also develops an alternative estimation method with closed-form expressions based on marginal distributions, and derives its asymptotic properties. Compared with variances of the MLEs in the finite and large sample situations, the alternative estimator performs very well, especially when the correlation between X and Y is small.

Original languageEnglish (US)
Pages (from-to)323-336
Number of pages14
JournalAustralian and New Zealand Journal of Statistics
Volume42
Issue number3
StatePublished - Sep 2000
Externally publishedYes

Fingerprint

Singular Distribution
Shock Model
Censored Data
Order Statistics
Parameter Estimation
Bivariate Exponential Distribution
Existence-uniqueness
Stopping Time
Strong Consistency
Alternatives
Parallel Systems
Marginal Distribution
Maximum Likelihood Estimate
Statistical Inference
Maximum Likelihood Estimation
Maximum Likelihood Estimator
Iterative Algorithm
Asymptotic distribution
Asymptotic Properties
Parameter Space

Keywords

  • Asymptotics
  • Bivariate exponential
  • Censored data
  • Reliability

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Parameter estimation for bivariate shock models with singular distribution for censored data with concomitant order statistics. / Chen, Di; Li, Chin-Shang; Lu, Jye Chyi; Park, Jinho.

In: Australian and New Zealand Journal of Statistics, Vol. 42, No. 3, 09.2000, p. 323-336.

Research output: Contribution to journalArticle

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