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Journals / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 3

Estimation of P(Y<X) for the Levy distribution

Hossein NAJARZADEGAN
Saman BABII
Saralees NADARJAH
Sadegh REZAEI
Pages
957–972
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Theirperformance with respect to relative biases, relative mean squared errors, coverage probabilities, and coverage lengths is assessed by simulation studies and a real data application

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Three point estimators and two interval estimators of P (Y < X) arederived when X and Y are independent Lévy random variables.
📊
Key Findings & Data:Three point estimators and two interval estimators of P (Y < X) arederived when X and Y are independent Lévy random variables.
💡
Conclusion & Impact:Theirperformance with respect to relative biases, relative mean squared errors, coverage probabilities, and coverage lengths is assessed by simulation studies and a real data application
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Three point estimators and two interval estimators of P (Y < X) arederived when X and Y are independent Lévy random variables. Theirperformance with respect to relative biases, relative mean squared errors, coverage probabilities, and coverage lengths is assessed by simulation studies and a real data application

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Cite This Article

NAJARZADEGAN, H., BABII, S., NADARJAH, S., REZAEI, S. (2022). Estimation of P(Y<X) for the Levy distribution. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 3, 957–972. https://ajindex.com/articles/530037

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References (17)

  1. Alfonso, L., Mansilla, R., Terrero-Escalante, C.A. On the scaling of the distribution of daily price uctuations in the Mexican nancial market index, Physica A Statistical Mechanics and Its Applications, 391, 2990-2996, 2012.
  2. Ali, M.M., Nadarajah, S., Woo, J.S. On the ratio X/(X + Y ) for Weibull and Lévy distri- butions, Journal of the Korean Statistical Society, 34, 11-20, 2005.
  3. Ali, M.M., Woo, J.S. Inference on reliability P (X _____ Y ) in the Lévy distribution, Mathe- matical and Computer Modeling, 41, 965-971, 2005.
  4. Awad, A.M., Gharraf, M.K. Estimation of P (Y _____ X) in the Burr case: A comparative study, Communications in Statistics - Simulation and Computation, 15, 389-403, 1986.
  5. Babayi, S., Khorram, E., Tondro, F. Inference of R = P [X _____ Y ] for generalized logistic distribution, Statistics, 48, 862-871, 2014.
  6. Barndor -Nielsen, O.E. Inference on full and partial parameters, based on the standardized signed log-likelihood ratio, Biometrika, 73, 307-322, 1986.
  7. Barndor -Nielsen, O.E. Modi ed signed log-likelihood ratio, Biometrika, 78, 557-563, 1991. [8] Casella, G. Statistical Inference, second edition. Duxbury Press, 2001.
  8. Chen, M.-H., Shao, Q.-M. Monte Carlo estimation of Bayesian credible and HPD intervals, Journal of Computational and Graphical Statistics, 8, 69-92, 1999.
  9. Congdon, P. Bayesian Statistical Modelling. John Wiley and Sons, New York, 2007.
  10. Constantine, K., Tse, S.K., Karson, M. Estimation of P (Y _____ X) in the gamma case, Communications in Statistics - Simulation and Computation, 15, 365-388, 1986.
  11. Davison, A.C. Statistical Models. Cambridge University Press, Cambridge, 2003.
  12. Dorfman, J.H., Karali, B. Do farmers hedge optimally or by habit? A Bayesian partial- adjustment model of farmer hedging, Journal of Agricultural and Applied Economics, 42, 791-803, 2010.
  13. Downtown, F. The estimation of Pr(Y _____ X) in the normal case, Technometrics, 15, 551-558, 1973.
  14. Efron, B. The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF Re- gional Conference Series in Applied Mathematics, 38, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1982.
  15. Felsenstein, J. Taking variation of evolutionary rates between sites into account in inferring phylogenies, Journal of Molecular Evolution, 53, 447-455, 2001.
  16. Genc, A.I. Estimation of P (X > Y ) with Topp-Leone distribution, Journal of Statistical Computation and Simulation, 83, 326-339, 2013.
  17. Gradshteyn, I.S., Ryzhik, I.M. Table of Integrals, Series, and Product