Point and Interval Estimation for Bivariate Normal Distribution Based on Progressively Type-II Censored Data

ABSTRACT

The maximum likelihood estimates (MLEs) of parameters of a bivariate normal distribution are derived based on progressively Type-II censored data. The asymptotic variances and covariances of the MLEs are derived from the Fisher information matrix. Using the asymptotic normality of MLEs and the asymptotic variances and covariances derived from the Fisher information matrix, interval estimation of the parameters is discussed and the probability coverages of the 90% and 95% confidence intervals for all the parameters are then evaluated by means of Monte Carlo simulations. To improve the probability coverages of the confidence intervals, especially for the correlation coefficient, sample-based Monte Carlo percentage points are determined and the probability coverages of the 90% and 95% confidence intervals obtained using these percentage points are evaluated and shown to be quite satisfactory. Finally, an illustrative example is presented.

Keywords:

• Asymptotic variance-covariance
• Concomitants of order statistics
• Fisher information matrix
• Maximum likelihood estimates
• Probability coverages
• Progressive Type-II censoring
• Sample-based Monte Carlo percentage points

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62G30

Notes

^†For simplicity of notation, progressive censoring scheme 0, 0, 0, 0, 0, 0, 0, 0, 0, 10 will be denoted as 9*0, 10.