zbMATH — the first resource for mathematics

On bilinear hazard quantile functions. (English) Zbl 1325.62190
Summary: We introduce and study a class of distributions with bilinear hazard quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. The estimators of the parameters of the class of distributions, using method of L-moments are derived. We apply the proposed class of distributions to a real data set.

62N05 Reliability and life testing
68M15 Reliability, testing and fault tolerance of networks and computer systems
Full Text: DOI
[1] Crow, L.H.: On the initial system reliability. In: Proceedings of the Annual Reliability and Maintainability Symposium, pp. 115-119 (1986) · Zbl 1154.60017
[2] Gilchrist, W.: Statistical Modelling with Quantile Functions. CRC Press, London (2000) · Zbl 1061.62548
[3] Hankin, RKS; Lee, A, A new family of non-negative distributions, Aust. N. Z. J. Stat., 48, 67-78, (2006) · Zbl 1109.62009
[4] Hosking, J.R.M.: L-Moments: analysis and estimation of distributions using linear combinations of order statistics. J. R. Stat. Soc. Ser. B (Methodol.) 52, 105-124 (1990) (Wiley for the Royal Statistical Society) · Zbl 0703.62018
[5] Hosking, J.R.M.: Some theoretical result concerning L-moments, research report, rc 14492 (revised). IBM Research Division, York Town Heights, New York (1996) · Zbl 1188.62293
[6] Kupka, J; Loo, S, The hazard and vitality measures of ageing, J. Appl. Probab., 26, 532-542, (1989) · Zbl 0681.60091
[7] Lai, C.D., Xie, M.: Stochastic Ageing and Dependence for Reliability. Springer, New York (2006) · Zbl 1098.62130
[8] Lyu, M.R.: Handbook of Software Reliability Engineering. Computer Society Press, IEEE, Los Alamitos (1996)
[9] Midhu, N.N., Sankaran, P.G., Nair, N.U.: A class of distributions with linear mean residual quantile function and it’s generalizations. Stat. Methodol. 15, 1-24 (2013) · Zbl 07035613
[10] Midhu, N.N., Sankaran, P.G., Nair, N.U.: A class of distributions with linear hazard quantile function. Commun. Stat. Theory Methods (2014). doi:10.1080/03610926.2012.705211 · Zbl 1302.62030
[11] Moranda, P.B.: Prediction of software reliability during debugging. In: Proceedings of the Annual Reliability and Maintainability Symposium, Washington, D.C., pp. 327-332 (1975) · Zbl 1167.62031
[12] Musa, J.D.: Software reliability data, data and analysis center for Software, 1950-01. https://www.thedacs.com/databases/sled/swrel.php (1980) · Zbl 0681.60091
[13] Musa, J.D.: Software reliability data, report and database available from data and analysis center for software. Rome Air Development Center, Rome (1985)
[14] Nair, NU; Sankaran, PG, Quantile-based reliability analysis, Commun. Stat. Theory Methods, 38, 222-232, (2009) · Zbl 1292.62025
[15] Nair, NU; Sankaran, PG; Vineshkumar, B, Total time on test transforms of order n and their implications in reliability analysis, J. Appl. Probab., 45, 1126-1139, (2008) · Zbl 1154.60017
[16] Nair, NU; Vineshkumar, B, L-moments of residual life, J. Stat. Plan. Inference, 140, 2618-2631, (2010) · Zbl 1188.62293
[17] Nair, NU; Vineshkumar, B, Ageing concepts: an approach based on quantile function, Stat. Probab. Lett., 81, 2016-2025, (2011) · Zbl 1225.62138
[18] Nair, NU; Sankaran, PG; Vineshkumar, B, Characterization of distributions by properties of truncated gini index and Mean difference, Metron, 70, 173-191, (2012) · Zbl 1302.62025
[19] Nair, N.U., Sankaran, P.G., Balakrishanan, N.: Quantile Based Reliability Analysis. Springer, Birkhauser Verlag GmbH, New York (2013) · Zbl 1306.62019
[20] Parzen, E, Non parametric statistical data modeling, J. Am. Stat. Assoc., 74, 105, (1979) · Zbl 0407.62001
[21] Sankaran, PG; Nair, NU, Nonparametric estimation of hazard quantile function, J. Nonparametr. Stat., 21, 757-767, (2009) · Zbl 1167.62031
[22] Sankarasubramanian, A., Srinivasan, K.: Investigation and comparison of sampling properties of l-moments and conventional moments. J. Hydrol. 218(1-2), 13-34 (1999)
[23] Schick, G.J., Wolverton, R.W.: Assessment of Software Reliability. In: Vorträge der jahrestagung 1972 dgor/Papers of the Annual Meeting 1972, pp. 395-422. Springer, New York (1973) · Zbl 0312.68015
[24] Xie, M.: Software Reliability Modelling, vol. 1. World Scientific Publishing Company Incorporated, Singapore (1991) · Zbl 0824.68025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.