Kundu, Debasis; Raqab, Mohammad Z. Generalized Rayleigh distribution: different methods of estimations. (English) Zbl 1429.62449 Comput. Stat. Data Anal. 49, No. 1, 187-200 (2005). Summary: Recently, J. G. Surles and W. J. Padgett [Lifetime Data Anal. 7, No. 2, 187–200, (2001; Zbl 0984.62082)] introduced two-parameter Burr Type X distribution, which can also be described as generalized Rayleigh distribution. It is observed that this particular skewed distribution can be used quite effectively in analyzing lifetime data. Different estimation procedures have been used to estimate the unknown parameter(s) and their performances are compared using Monte Carlo simulations. Cited in 63 Documents MSC: 62N05 Reliability and life testing 62E10 Characterization and structure theory of statistical distributions 62G30 Order statistics; empirical distribution functions Keywords:maximum likelihood estimators; modified moment estimators; Fisher information matrix; asymptotic distribution; order statistics; percentile-based estimator; least-squares estimators; L-moment estimators PDF BibTeX XML Cite \textit{D. Kundu} and \textit{M. Z. Raqab}, Comput. Stat. Data Anal. 49, No. 1, 187--200 (2005; Zbl 1429.62449) Full Text: DOI References: [1] Ahmad, K.E.; Fakhry, M.E.; Jaheen, Z.F., Empirical Bayes estimation of \(P(Y < X)\) and characterization of burr-type X model, J. statist. plann. inference, 64, 297-308, (1997) · Zbl 0915.62001 [2] Burr, I.W., Cumulative frequency distribution, Ann. math. statist., 13, 215-232, (1942) · Zbl 0060.29602 [3] David, H.A., Order statistics, (1981), Wiley New York [4] Gupta, R.D.; Kundu, D., Generalized exponential distributiondifferent methods of estimation, J. statist. comput. simulation, 59, 315-337, (2002) [5] Hosking, J.R.M., L-momentanalysis and estimation of distributions using linear combinations of order statistics, J. roy. statist. soc. ser. B, 52, 105-124, (1990) · Zbl 0703.62018 [6] Jaheen, Z.F., Bayesian approach to prediction with outliers from the burr type X model, Microelectron. rel., 35, 45-47, (1995) [7] Jaheen, Z.F., Empirical Bayes estimation of the reliability and failure rate functions of the burr type X failure model, J. appl. statist. sci., 3, 281-288, (1996) · Zbl 1054.62593 [8] Johnson, N.L., Kotz, S., Balakrishnan, N., 1995. Continuous Univariate Distribution, vol. 1, second ed. Wiley, New York. [9] Kao, J.H.K., Computer methods for estimating Weibull parameters in reliability studies, Trans. IRE-reliability quality control, 13, 15-22, (1958) [10] Kao, J.H.K., A graphical estimation of mixed Weibull parameters in life testing electron tube, Technometrics, 1, 389-407, (1959) [11] Karian, Z.A.; Dudewicz, E.J., Modern statistical systems and GPSS simulations, (1999), CRC Press Florida [12] Mann, N.R.; Schafer, R.E.; Singpurwalla, N.D., Methods for statistical analysis of reliability and life data, (1974), Wiley New York · Zbl 0339.62070 [13] Mudholkar, G.S.; Srivastava, D.K., Exponentiated Weibull family for analyzing bathtub failure data, IEEE trans. reliability, 42, 299-302, (1993) · Zbl 0800.62609 [14] Mudholkar, G.S.; Srivastava, D.K.; Freimer, M., The exponentiated Weibull family; a re-analysis of the bus motor failure data, Technometrics, 37, 436-445, (1995) · Zbl 0900.62531 [15] Raqab, M.Z., Order statistics from the burr type X model, Comput. math. appl., 36, 111-120, (1998) · Zbl 0933.62042 [16] Raqab, M.Z., Kundu, D., 2003. Burr Type X distribution; revisited. Submitted for publication. [17] Rodriguez, R.N., A guide to burr type XII distributions, Biometrika, 64, 129-134, (1977) · Zbl 0354.62017 [18] Sartawi, H.A.; Abu-Salih, M.S., Bayes prediction bounds for the burr type X model, Commun. statist. theory methods, 20, 2307-2330, (1991) · Zbl 0850.62288 [19] Surles, J.G.; Padgett, W.J., Inference for \(P(Y < X)\) in the burr type X model, J. appl. statist. sci., 225-238, (1998) · Zbl 0911.62092 [20] Surles, J.G.; Padgett, W.J., Inference for reliability and stress-strength for a scaled burr type X distribution, Lifetime data anal., 7, 187-200, (2001) · Zbl 0984.62082 [21] Surles, J.G., Padgett, W.J., 2004. Some properties of a scaled Burr type X distribution. J. Statist. Plann. Inference, to appear · Zbl 1058.62017 [22] Swain, J.; Venkatraman, S.; Wilson, J., Least-squares estimation of distribution function in Johnson’s translation system, J. statist. comput. simulation, 29, 271-297, (1988) [23] Wongo, D.R., Maximum likelihood methods for Fitting the burr type XII distribution to multiply (progressively) censored life test data, Metrika, 40, 203-210, (1993) · Zbl 0775.62276 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.