Estimation of Stress-Strength Reliability for the Pareto Distribution Based on Upper Record Values

Rahmath Manzil Juvairiyya, Parameshwaranpillai Anilkumar


In this paper, the estimation of stress-strength reliability based on upper record values is considered when X and Y are independent random variables having a Pareto distribution with the same scale parameter and with different shape parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimators and the exact confidence interval of the stress-strength reliability are obtained. A Monte Carlo simulation study is conducted to investigate the merits of the proposed methods. A real data analysis is presented for illustrative purpose.


Stress-strength reliability; Record values; Pareto distribution; Maximum likelihood estimator; Bayes estimator

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B. C. ARNOLD, N. BALAKRISHNAN, H. N. NAGARAJA (1998). Records. John Wiley & Sons, Inc., New York.

A. ASGHARZADEH, R. VALIOLLAHI, M. Z. RAQAB (2017). Estimation of Pr(Y < X) for the two-parameter generalized exponential records. Communications in Statistics - Simulation and Computation, 46, no. 1, pp. 379–394.

A. BAKLIZI (2008). Estimation of Pr(X < Y) using record values in the one and two parameter exponential distributions. Communications in Statistics - Theory and Methods, 37, no. 5, pp. 692–698.

A. BAKLIZI (2012). Inference on Pr(X < Y) in the two-parameter Weibull model based on records. ISRN Probability and Statistics, 2012, pp. 1–11.

M. BASIRAT, S. BARATPOUR, J. AHMADI (2016). On estimation of stress–strength parameter using record values from proportional hazard rate models. Communications in Statistics - Theory and Methods, 45, no. 19, pp. 5787–5801.

K. N. CHANDLER (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B, 14, no. 2, pp. 220–228.

M. CROWDER (2000). Tests for a family of survival models based on extremes. In N. LIMNIOS, M. NIKULIN (eds.), Recent Advances in Reliability Theory Methodology, Practice, and Inference, Birkhäuser Boston, Boston, MA, pp. 307–321.

S. KOTZ, I. A. P. LUMELSKII, M. PENSKY (2003). The Stress-Strength Model and its Generalizations: Theory and Applications. World Scientific, Singapore.

D. V. LINDLEY (1980). Approximate Bayesian methods. Trabajos de Estadistica Y de Investigacion Operativa, 31, no. 1, pp. 223–245.

S. REZAEI, R. TAHMASBI, M.MAHMOODI (2010). Estimation of P(Y < X) for generalized Pareto distribution. Journal of Statistical Planning and Inference, 140, no. 2, pp. 480–494.

B. TARVIRDIZADE, M. AHMADPOUR (2016). Estimation of the stress-strength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values. Statistical Methodology, 31, pp. 58–72.

DOI: 10.6092/issn.1973-2201/8242