Selecting a Component with Longer Mean Life Time in Bivariate Pareto Models
ABSTRACT
In any parallel system, selecting a component with longer mean lifetime is of interest to the researchers. Hanagal (1997) [1] discussed selection procedures for a two-component system with bivariate exponential (BVE) models. In this paper, the problem of selecting a better component with reference to its mean life time under bivariate Pareto (BVP) models is considered. Three selection procedures based on sample proportions, sample means and maximum likelihood estimators (MLE) are proposed. The probability of correct selection for the proposed procedures is evaluated through Monte Carlo simulation using normal approximation. The asymptotic relative efficiency (ARE) of the proposed procedures is presented to facilitate the evaluation of the performance of procedures.
In any parallel system, selecting a component with longer mean lifetime is of interest to the researchers. Hanagal (1997) [1] discussed selection procedures for a two-component system with bivariate exponential (BVE) models. In this paper, the problem of selecting a better component with reference to its mean life time under bivariate Pareto (BVP) models is considered. Three selection procedures based on sample proportions, sample means and maximum likelihood estimators (MLE) are proposed. The probability of correct selection for the proposed procedures is evaluated through Monte Carlo simulation using normal approximation. The asymptotic relative efficiency (ARE) of the proposed procedures is presented to facilitate the evaluation of the performance of procedures.
KEYWORDS
Asymptotic Relative Efficiency (ARE), Better Component, Bivariate Pareto, Probability of Correct Selection
Asymptotic Relative Efficiency (ARE), Better Component, Bivariate Pareto, Probability of Correct Selection
Cite this paper
Pandit, P. and Joshi, S. (2015) Selecting a Component with Longer Mean Life Time in Bivariate Pareto Models. Open Journal of Statistics, 5, 355-359. doi: 10.4236/ojs.2015.55037.
Pandit, P. and Joshi, S. (2015) Selecting a Component with Longer Mean Life Time in Bivariate Pareto Models. Open Journal of Statistics, 5, 355-359. doi: 10.4236/ojs.2015.55037.
References
[1] Hanagal, D.D. (1997) Selection of a Better Component in Bivariate Exponential Models. Journal of the Italian Statistical Association, 5, 453-460. [2] Freund, J.E. (1961) A Bivariate Extension of the Exponential Distribution. Journal of the American Statistical Association, 56, 971-977.
http://dx.doi.org/10.1080/01621459.1961.10482138 [3] Marshall, A.W. and Olkin, I. (1967) A Multivariate Exponential Distribution. Journal of the American Statistical Association, 62, 30-44.
http://dx.doi.org/10.1080/01621459.1967.10482885 [4] Block, H.W. and Basu, A.P. (1974) A Continuous Bivariate Exponential Extension. Journal of the American Statistical Association, 69, 1031-1037. [5] Hyakuntake, H. (1992) Selecting the Better Component of a Bivariate Exponential Distribution. Statistics and Decisions, 10, 153-162. [6] Veenus, P and Nair, K.R.M. (1994) Characterization of a Bivariate Pareto Distribution. Journal of the Indian Statistical Association, 32, 15-20. [7] Hanagal, D.D. (1997) Note on Estimation of Reliability under Bivariate Pareto Stress-Strength Model. Statistical Papers, 38, 453-459.
http://dx.doi.org/10.1007/BF02926000
[1] Hanagal, D.D. (1997) Selection of a Better Component in Bivariate Exponential Models. Journal of the Italian Statistical Association, 5, 453-460. [2] Freund, J.E. (1961) A Bivariate Extension of the Exponential Distribution. Journal of the American Statistical Association, 56, 971-977.
http://dx.doi.org/10.1080/01621459.1961.10482138 [3] Marshall, A.W. and Olkin, I. (1967) A Multivariate Exponential Distribution. Journal of the American Statistical Association, 62, 30-44.
http://dx.doi.org/10.1080/01621459.1967.10482885 [4] Block, H.W. and Basu, A.P. (1974) A Continuous Bivariate Exponential Extension. Journal of the American Statistical Association, 69, 1031-1037. [5] Hyakuntake, H. (1992) Selecting the Better Component of a Bivariate Exponential Distribution. Statistics and Decisions, 10, 153-162. [6] Veenus, P and Nair, K.R.M. (1994) Characterization of a Bivariate Pareto Distribution. Journal of the Indian Statistical Association, 32, 15-20. [7] Hanagal, D.D. (1997) Note on Estimation of Reliability under Bivariate Pareto Stress-Strength Model. Statistical Papers, 38, 453-459.
http://dx.doi.org/10.1007/BF02926000