{
"id": "https://doi.org/10.5281/zenodo.1100604",
"doi": "10.5281/ZENODO.1100604",
"url": "https://zenodo.org/record/1100604",
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"resourceTypeGeneral": "Text"
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"creators": [
{
"name": "F. Z. Doğru",
"affiliation": []
},
{
"name": "O. Arslan",
"affiliation": []
}
],
"titles": [
{
"title": "Alternative Robust Estimators For The Shape Parameters Of The Burr Xii Distribution"
}
],
"publisher": {
"name": "Zenodo"
},
"container": {},
"subjects": [
{
"subject": "Burr XII distribution"
},
{
"subject": "robust estimator"
},
{
"subject": "M-estimator"
},
{
"subject": "maximum likelihood"
},
{
"subject": "least squares."
}
],
"contributors": [],
"dates": [
{
"date": "2015-04-02",
"dateType": "Issued"
}
],
"publicationYear": 2015,
"language": "en",
"identifiers": [
{
"identifier": "https://zenodo.org/record/1100605",
"identifierType": "URL"
}
],
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"rightsList": [
{
"rights": "Creative Commons Attribution 4.0",
"rightsUri": "https://creativecommons.org/licenses/by/4.0"
},
{
"rights": "Open Access",
"rightsUri": "info:eu-repo/semantics/openAccess"
}
],
"descriptions": [
{
"description": "In general, classical methods such as maximum
\nlikelihood (ML) and least squares (LS) estimation methods are used
\nto estimate the shape parameters of the Burr XII distribution.
\nHowever, these estimators are very sensitive to the outliers. To
\novercome this problem we propose alternative robust estimators
\nbased on the M-estimation method for the shape parameters of the
\nBurr XII distribution. We provide a small simulation study and a real
\ndata example to illustrate the performance of the proposed estimators
\nover the ML and the LS estimators. The simulation results show that
\nthe proposed robust estimators generally outperform the classical
\nestimators in terms of bias and root mean square errors when there
\nare outliers in data.",
"descriptionType": "Abstract"
},
{
"description": "{\"references\": [\"I. W. Burr, \\\"Cumulative frequency functions,\\\" Ann. Math. Stat., vol. 13,\\nno. 2, pp. 215-232, June 1942.\", \"R. N. Rodriguez, and B. Y. Taniguchi, \\\"A new statistical model for\\npredicting customer octane Satisfaction using trained-rater\\nobservations,\\\" Trans. Soc. Automotive Eng., pp. 4213\\u20134235, 1980.\", \"S. K. Singh, and G. S. Maddala, \\\"A function for size distribution of\\nincomes,\\\" Econometrica, vol. 44, pp. 963\\u2013970, 1976.\", \"J. B. McDonald, and D. O. Richards, \\\"Model selection: Some\\ngeneralized distributions,\\\" Commun. Stat-Theor M., vol. 16, 1987;\\n(4):1049-1074.\", \"P. W. Jr. Mielke, and E. S. Johnson, \\\"Some generalized beta\\ndistributions of the second kind having desirable application features in\\nhydrology and meteorology,\\\" Water Resour. Res., vol. 10, pp. 223-226,\\nApril 1974.\", \"R. D. Cook, and M. E. Johnson, \\\"Generalized Burr-Pareto-Logistic\\ndistributions with applications to a uranium exploration data set,\\\"\\nTechnometrics, vol. 28, no. 2, pp. 123-131, May 1986.\", \"D. R. Wingo, \\\"Maximum likelihood methods for fitting the Burr XII\\ndistribution to life test data,\\\" Biometrical J., vol. 25, pp. 77-84, 1983.\", \"D. R. Wingo, \\\"Maximum likelihood estimation of Burr XII distribution\\nparameters under Type II censoring,\\\" Microelectron Reliab., vol. 33, pp.\\n1251-1257, July 1993.\", \"F. K. Wang, J. B. Keats, and W. J. Zimmer, \\\"Maximum likelihood\\nestimation of the Burr XII distribution with censored and uncensored\\ndata,\\\" Microelectron. Reliab., vol. 36, pp. 359-362, March 1996.\\n[10] W. J. Zimmer, J. B. Keats, and F. K. Wang, \\\"The Burr XII distribution\\nin reliability analysis,\\\" J. Qual. Tech., vol. 30, pp. 386-394, Oct. 1998.\\n[11] I. W. Burr, and P. J. Cislak, \\\"On a general system of distributions: I. Its\\ncurve-shape characteristics; II. The sample median,\\\" J. Am. Statist.\\nAssoc., vol. 63, no. 322, pp. 627-635, June 1968.\\n[12] E. K. Al-Hussaini, \\\"A characterization of the Burr type XII\\ndistribution,\\\" Appl. Math. Lett., vol. 4, no. 1, pp. 59-61, 1991.\\n[13] R. N. Rodriguez, \\\"A guide to the Burr XII distributions,\\\" Biometrika,\\nvol. 64, no. 1, pp. 129-134, April 1977.\\n[14] P. R. Tadikamalla, \\\"A look at the Burr and related distributions,\\\" Int.\\nStat. Rev., vol. 48, no. 3, pp. 337-344, Dec. 1980.\\n[15] A. M. Hossain, and S. K. Nath, \\\"Estimation of parameters in the\\npresence of outliers for a Burr XII distribution,\\\" Commun. Stat-Theor\\nM., vol. 26, pp. 813-827, 1997.\\n[16] A. Shah, and D. V. Gokhale, \\\"On maximum product of spacings (mps)\\nestimation for Burr XII distributions,\\\" Commun. Stat-Simul. C., vol. 22,\\npp. 615-641, 1993.\\n[17] F. K. Wang, and Y. F. Cheng, \\\"Robust regression for estimating the\\nBurr XII parameters with outliers,\\\" J. Appl. Stat., vol. 37, no. 5, pp. 807-\\n819, May 2010.\\n[18] F.Z. Do\\u011fru, and O. Arslan, \\\"Optimal B-Robust Estimators for the\\nParameters of the Burr XII Distribution,\\\" revised, 2015.\\n[19] P. J. Huber, \\\"Robust estimation of a location parameter,\\\" Ann. Math.\\nStatist., vol. 35, pp. 73-101, 1964.\\n[20] D. N. P. Murthy, M. Xie, and R. Jiang, Weibull models, New York:\\nWiley, 2004.\\n[21] R. B. Silva, and G. M. Cordeiro, \\\"The Burr XII power series\\ndistributions: A new compounding family,\\\" Braz. J. Probab. Stat., to be\\npublished, 2015.\"]}",
"descriptionType": "Other"
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