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A new Lifetime Distribution Based on the Transmuted First Two Lower Records

Year 2022, Volume: 43 Issue: 3, 534 - 542, 30.09.2022

Tenzile Erbayram Ümmügülsüm Yıldırım Yunus Akdoğan

https://doi.org/10.17776/csj.1094289

Abstract

This article introduces a new lifetime distribution by merging the first two lower records based on exponential distribution and discusses the different features of the distribution. Statistical inferences about the distribution parameters are discussed with three estimation methods, namely maximum likelihood, least squares, and weighted least squares. Monte Carlo simulation study is performed to evaluate of these estimators based on mean square errors estimation, mean absolute deviation, and mean relative errors of estimation for a sample of different sizes. A distribution simulation analysis based on real data is provided to demonstrate the adaptability of the proposed model.

Keywords

Lower record value Lifetime distribution Monte Carlo simulation Estimation.

References

  • [1] Azzalini A., A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12 (1985) 171-178.
  • [2] Mudholkar G.S., Srivastava D.K., Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42 (1993) 299-302.
  • [3] Marshall A.W., Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997) 641-652.
  • [4] Eugene N., Lee C., Famoye F., Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31 (2002) 497-512.
  • [5] Mahdavi A., Kundu D., A new method for generating distributions with an application to exponential distribution, Communications in Statistics-Theory and Methods, 46 (2017) 6543-6557.
  • [6] Karakaya K., Kınacı I., Akdoğan Y., Kuş C., A new family of distributions, Hacettepe Journal of Mathematics and Statistics, 46 (2017) 303-314.
  • [7] Shaw W.T., Buckley I.R., The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions, (2007) Submitted, Feb, 7, 64.
  • [8] Shaw W.T., Buckley I.R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv preprint arXiv:0901.0434. (2009).
  • [9] Alizadeh M., Merovci F., Hamedani G.G., Generalized transmuted family of distributions: properties and applications, Hacet. J. Math. Stat., 46 (2017) 645–667.
  • [10] Granzotto D.C.T., Louzada F., Balakrishnan N., Cubic rank transmuted distributions: inferential issues and applications, Journal Statistical Computation and Simulation, 87(14) (2017) 2760–2778.
  • [11] Balakrishnan N., He M., A Record-Based Transmuted Model, Under review, Advance Online Publication (2019).
  • [12] Tanış C., Saraçoğlu B., On the record-based transmuted model of Balakrishnan and He based on Weibull distribution, Communications in Statistics - Simulation and Computation, In press, (2020).
  • [13] Tanış C., Saraçoğlu B., Kuş C., Pekgör A., Karakaya, K., Transmuted lower record type Fréchet distribution with lifetime regression analysis based on type I-censored data, Journal of Statistical Theory and Applications, 20(1) (2021) 86-96.
  • [14] Tanış C., Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications, Ricerche di Matematica, In press, (2022)
  • [15] Taniş C., Transmuted lower record type power functıon dıstrıbutıon, Journal of Science and Arts, 21(4) (2021) 951-960.
  • [16] Choulakian V., Stephens M.A., Goodness-of-fit tests for the generalized Pareto distribution, Technometrics, 43(4) (2001) 478-484.
  • [17] Riffi M.I., Ansari S.I., Hamdan M.S., A generalized transmuted Frechet distribution, Journal of Statistics Applications & Probability, 8(2) (2019) 1-10.

Year 2022, Volume: 43 Issue: 3, 534 - 542, 30.09.2022

Tenzile Erbayram Ümmügülsüm Yıldırım Yunus Akdoğan

https://doi.org/10.17776/csj.1094289

Abstract

References

  • [1] Azzalini A., A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12 (1985) 171-178.
  • [2] Mudholkar G.S., Srivastava D.K., Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42 (1993) 299-302.
  • [3] Marshall A.W., Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997) 641-652.
  • [4] Eugene N., Lee C., Famoye F., Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31 (2002) 497-512.
  • [5] Mahdavi A., Kundu D., A new method for generating distributions with an application to exponential distribution, Communications in Statistics-Theory and Methods, 46 (2017) 6543-6557.
  • [6] Karakaya K., Kınacı I., Akdoğan Y., Kuş C., A new family of distributions, Hacettepe Journal of Mathematics and Statistics, 46 (2017) 303-314.
  • [7] Shaw W.T., Buckley I.R., The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions, (2007) Submitted, Feb, 7, 64.
  • [8] Shaw W.T., Buckley I.R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv preprint arXiv:0901.0434. (2009).
  • [9] Alizadeh M., Merovci F., Hamedani G.G., Generalized transmuted family of distributions: properties and applications, Hacet. J. Math. Stat., 46 (2017) 645–667.
  • [10] Granzotto D.C.T., Louzada F., Balakrishnan N., Cubic rank transmuted distributions: inferential issues and applications, Journal Statistical Computation and Simulation, 87(14) (2017) 2760–2778.
  • [11] Balakrishnan N., He M., A Record-Based Transmuted Model, Under review, Advance Online Publication (2019).
  • [12] Tanış C., Saraçoğlu B., On the record-based transmuted model of Balakrishnan and He based on Weibull distribution, Communications in Statistics - Simulation and Computation, In press, (2020).
  • [13] Tanış C., Saraçoğlu B., Kuş C., Pekgör A., Karakaya, K., Transmuted lower record type Fréchet distribution with lifetime regression analysis based on type I-censored data, Journal of Statistical Theory and Applications, 20(1) (2021) 86-96.
  • [14] Tanış C., Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications, Ricerche di Matematica, In press, (2022)
  • [15] Taniş C., Transmuted lower record type power functıon dıstrıbutıon, Journal of Science and Arts, 21(4) (2021) 951-960.
  • [16] Choulakian V., Stephens M.A., Goodness-of-fit tests for the generalized Pareto distribution, Technometrics, 43(4) (2001) 478-484.
  • [17] Riffi M.I., Ansari S.I., Hamdan M.S., A generalized transmuted Frechet distribution, Journal of Statistics Applications & Probability, 8(2) (2019) 1-10.
There are 17 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Tenzile Erbayram 0000-0002-3275-120X

Ümmügülsüm Yıldırım 0000-0001-6780-6373

Yunus Akdoğan 0000-0003-3520-7493

Publication Date September 30, 2022
Submission Date March 28, 2022
Acceptance Date June 16, 2022
Published in Issue Year 2022Volume: 43 Issue: 3

Cite

APA Erbayram, T., Yıldırım, Ü., & Akdoğan, Y. (2022). A new Lifetime Distribution Based on the Transmuted First Two Lower Records. Cumhuriyet Science Journal, 43(3), 534-542. https://doi.org/10.17776/csj.1094289
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