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Year 2022, Volume: 35 Issue: 2, 731 - 746, 01.06.2022

Mohammed Elgarhy Amal Soliman Heba Nagy

https://doi.org/10.35378/gujs.776277
Cited By: 4

Abstract

References

  • [1] Topp, C. W., Leone, F. C., “A family of J-shaped frequency functions”, Journal of the American Statistical Association, 50(269): 209–219, (1955).
  • [2] Nadarajah, S., Kotz, S., “Moments of some J-shaped distributions”, Journal of Applied Statistics, 30(3): 311–317, (2003).
  • [3] Kotz, S., Dorp, J. R. v., “Beyond Beta: Other Continuous Families of Distributions With Bounded Support And Applications”, Singapore, World Scientific, (2004).
  • [4] Ghitany, M. E., Kotz, S., Xie, M., “On some reliability measures and their stochastic orderings for the Topp–Leone distribution”, Journal of Applied Statistics, 32(7): 715–722, (2005).
  • [5] Genç, A. İ., “Moments of order statistics of Topp-Leone distribution”, Statistical Papers, 53(1): 117–131, (2010).
  • [6] Abbas, S., Taqi, S. A., Mustafa, F., Murtaza, M., Shahbaz, M. Q., “Topp-Leone inverse Weibull distribution: theory and application”, European Journal of Pure and Applied Mathematics, 10(5): 1005–1022, (2017).
  • [7] Sudsuk, A., Bodhisuwan, W., “The Topp-Leone geometric distribution”, 12th International Conference on Mathematics, Statistics, and Their Applications (ICMSA): IEEE: 108–112, (2016).
  • [8] Yousof, H. M., Korkmaz, M. Ç., “Topp-Leone Nadarajah-Haghighi distribution”, İstatistikçiler Dergisi: İstatistik ve Aktüerya, 10(2): 119–127, (2017).
  • [9] Atem, B. A., Nasiru, S., Nantomah, K., “Topp–Leone linear exponential distribution”, Stochastics and Quality Control, 33(1): 31–43, (2018).
  • [10] Bantan, R. A., Jamal, F., Chesneau, C., Elgarhy, M., “A new power Topp–Leone generated family of distributions with applications”, Entropy, 21(12): 1177, (2019).
  • [11] Hassan, A. S., Elgarhy, M., Ahmad, Z., “Type II generalized Topp-Leone family of distributions: properties and applications”, Journal of Data Science, 17(4): 638–659, (2019).
  • [12] Bantan, R. A., Jamal, F., Chesneau, C., Elgarhy, M., “Type II power Topp-Leone generated family of distributions with statistical inference and applications”, Symmetry, 12(1): 1–24, (2020).
  • [13] Al-Marzouki, S., Jamal, F., Chesneau, C., Elgarhy, M., “Topp-Leone odd Fréchet generated family of distributions with applications to Covid-19 datasets”, CMES-Computer Modeling in Engineering and Sciences, 125: 437–458, (2020).
  • [14] Hassan, A. S., Elgarhy, M., Ragab, R., “Statistical properties and estimation of inverted Topp-Leone Distribution”, Journal of Statistics Applications & Probability, 9(2): 319–331, (2020).
  • [15] Hassan, A. S., Khaleel, M. A., Nassr, S. G., “Transmuted Topp-Leone power function distribution: Theory and application”, Journal of Statistics Applications & Probability, 10(1): 215–227, (2021).
  • [16] Hassan, A. S., Ismail, D. M., “Estimation of parameters of Topp-Leone inverse Lomax distribution in presence of right censored samples”, Gazi University Journal of Science, 34(4), (2021). DOI: 10.35378/gujs.773645
  • [17] Gündüz, S., Korkmaz, M. Ç., “A new unit distribution based on the unbounded Johnson distribution rule: The unit Johnson SU distribution”, Pakistan Journal of Statistics and Operation Research, 16(3): 471–490, (2020).
  • [18] Korkmaz, M. Ç., “The unit generalized half normal distribution: A new bounded distribution with inference and application”, University Politehnica Bucharest Scientific Bulltien Series A- Applied Mathematics and Physics, 82(2): 133–140, (2020).
  • [19] Korkmaz, M. Ç., “A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application”, Journal of Applied Statistics, 47(12): 2097–2119, (2020).
  • [20] Hassan, A. S., Sabry, M., Elsehetry, A., “Truncated power Lomax distribution with application to flood data”, Journal of Statistics Applications & Probability, 9(2): 347–359, (2020).
  • [21] Korkmaz, M. Ç., Chesneau, C., “On the unit Burr-XII distribution with the quantile regression modeling and applications”, Computational and Applied Mathematics, 40(1): 1–26, (2021).
  • [22] Shaked, M., Shanthikumar, J. G., “Stochastic Orders”, Springer Series in Statistics, New York, Springer, (2007).
  • [23] Johnson, N. L., Kotz, S., Balakrishnan, N., “Continuous Univariate Distributions”, (Vol. 2), New York John Wiley & Sons, Inc., (1995).
  • [24] MacDonald, P. D. M., “Comments and Queries Comment on "An estimation procedure for mixtures of distributions" by Choi and Bulgren”, Journal of the Royal Statistical Society. Series B (Methodological), 33(2): 326–329, (1971).
  • [25] 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”, IMA Conference on Computational Finance, De Morgan House, London: arXiv:0901.0434, (2009).
  • [26] Klein, J. P., Moeschberger, M. L., “Survival Analysis: Techniques for Censored and Truncated Data”, (second ed.), Springer-Verlag New York, Inc., (2006).
  • [27] Dumonceaux, R. H., Antle, C. E., “Discriminating between the log-normal and Weibull distribution”, Technometrics, 15(4): 923–926, (1973).

Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution

Year 2022, Volume: 35 Issue: 2, 731 - 746, 01.06.2022

Mohammed Elgarhy Amal Soliman Heba Nagy

https://doi.org/10.35378/gujs.776277
Cited By: 4

Abstract

We display the power Topp-Leone (PTL) distribution with two parameters. The following major features of the PTL distribution are investigated: quantile measurements, certain moment’s measures, residual life function, and entropy measure. Maximum likelihood, least squares, Cramer von Mises, and weighted least squares approaches are used to estimate the PTL parameters. A numerical illustration is prepared to compare the behavior of the achieved estimates. Data analysis is provided to scrutinize the flexibility of the PTL model matched with Topp-Leone distribution.

Keywords

Cramer von Mises estimators Maximum likelihood estimators Moments Topp-Leone distribution

References

  • [1] Topp, C. W., Leone, F. C., “A family of J-shaped frequency functions”, Journal of the American Statistical Association, 50(269): 209–219, (1955).
  • [2] Nadarajah, S., Kotz, S., “Moments of some J-shaped distributions”, Journal of Applied Statistics, 30(3): 311–317, (2003).
  • [3] Kotz, S., Dorp, J. R. v., “Beyond Beta: Other Continuous Families of Distributions With Bounded Support And Applications”, Singapore, World Scientific, (2004).
  • [4] Ghitany, M. E., Kotz, S., Xie, M., “On some reliability measures and their stochastic orderings for the Topp–Leone distribution”, Journal of Applied Statistics, 32(7): 715–722, (2005).
  • [5] Genç, A. İ., “Moments of order statistics of Topp-Leone distribution”, Statistical Papers, 53(1): 117–131, (2010).
  • [6] Abbas, S., Taqi, S. A., Mustafa, F., Murtaza, M., Shahbaz, M. Q., “Topp-Leone inverse Weibull distribution: theory and application”, European Journal of Pure and Applied Mathematics, 10(5): 1005–1022, (2017).
  • [7] Sudsuk, A., Bodhisuwan, W., “The Topp-Leone geometric distribution”, 12th International Conference on Mathematics, Statistics, and Their Applications (ICMSA): IEEE: 108–112, (2016).
  • [8] Yousof, H. M., Korkmaz, M. Ç., “Topp-Leone Nadarajah-Haghighi distribution”, İstatistikçiler Dergisi: İstatistik ve Aktüerya, 10(2): 119–127, (2017).
  • [9] Atem, B. A., Nasiru, S., Nantomah, K., “Topp–Leone linear exponential distribution”, Stochastics and Quality Control, 33(1): 31–43, (2018).
  • [10] Bantan, R. A., Jamal, F., Chesneau, C., Elgarhy, M., “A new power Topp–Leone generated family of distributions with applications”, Entropy, 21(12): 1177, (2019).
  • [11] Hassan, A. S., Elgarhy, M., Ahmad, Z., “Type II generalized Topp-Leone family of distributions: properties and applications”, Journal of Data Science, 17(4): 638–659, (2019).
  • [12] Bantan, R. A., Jamal, F., Chesneau, C., Elgarhy, M., “Type II power Topp-Leone generated family of distributions with statistical inference and applications”, Symmetry, 12(1): 1–24, (2020).
  • [13] Al-Marzouki, S., Jamal, F., Chesneau, C., Elgarhy, M., “Topp-Leone odd Fréchet generated family of distributions with applications to Covid-19 datasets”, CMES-Computer Modeling in Engineering and Sciences, 125: 437–458, (2020).
  • [14] Hassan, A. S., Elgarhy, M., Ragab, R., “Statistical properties and estimation of inverted Topp-Leone Distribution”, Journal of Statistics Applications & Probability, 9(2): 319–331, (2020).
  • [15] Hassan, A. S., Khaleel, M. A., Nassr, S. G., “Transmuted Topp-Leone power function distribution: Theory and application”, Journal of Statistics Applications & Probability, 10(1): 215–227, (2021).
  • [16] Hassan, A. S., Ismail, D. M., “Estimation of parameters of Topp-Leone inverse Lomax distribution in presence of right censored samples”, Gazi University Journal of Science, 34(4), (2021). DOI: 10.35378/gujs.773645
  • [17] Gündüz, S., Korkmaz, M. Ç., “A new unit distribution based on the unbounded Johnson distribution rule: The unit Johnson SU distribution”, Pakistan Journal of Statistics and Operation Research, 16(3): 471–490, (2020).
  • [18] Korkmaz, M. Ç., “The unit generalized half normal distribution: A new bounded distribution with inference and application”, University Politehnica Bucharest Scientific Bulltien Series A- Applied Mathematics and Physics, 82(2): 133–140, (2020).
  • [19] Korkmaz, M. Ç., “A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application”, Journal of Applied Statistics, 47(12): 2097–2119, (2020).
  • [20] Hassan, A. S., Sabry, M., Elsehetry, A., “Truncated power Lomax distribution with application to flood data”, Journal of Statistics Applications & Probability, 9(2): 347–359, (2020).
  • [21] Korkmaz, M. Ç., Chesneau, C., “On the unit Burr-XII distribution with the quantile regression modeling and applications”, Computational and Applied Mathematics, 40(1): 1–26, (2021).
  • [22] Shaked, M., Shanthikumar, J. G., “Stochastic Orders”, Springer Series in Statistics, New York, Springer, (2007).
  • [23] Johnson, N. L., Kotz, S., Balakrishnan, N., “Continuous Univariate Distributions”, (Vol. 2), New York John Wiley & Sons, Inc., (1995).
  • [24] MacDonald, P. D. M., “Comments and Queries Comment on "An estimation procedure for mixtures of distributions" by Choi and Bulgren”, Journal of the Royal Statistical Society. Series B (Methodological), 33(2): 326–329, (1971).
  • [25] 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”, IMA Conference on Computational Finance, De Morgan House, London: arXiv:0901.0434, (2009).
  • [26] Klein, J. P., Moeschberger, M. L., “Survival Analysis: Techniques for Censored and Truncated Data”, (second ed.), Springer-Verlag New York, Inc., (2006).
  • [27] Dumonceaux, R. H., Antle, C. E., “Discriminating between the log-normal and Weibull distribution”, Technometrics, 15(4): 923–926, (1973).
There are 27 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Mohammed Elgarhy 0000-0002-1333-3862

Amal Soliman This is me 0000-0003-4442-8458

Heba Nagy 0000-0003-0262-205X

Publication Date June 1, 2022
Published in Issue Year 2022 Volume: 35 Issue: 2

Cite

APA Elgarhy, M., Soliman, A., & Nagy, H. (2022). Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution. Gazi University Journal of Science, 35(2), 731-746. https://doi.org/10.35378/gujs.776277
AMA Elgarhy M, Soliman A, Nagy H. Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution. Gazi University Journal of Science. June 2022;35(2):731-746. doi:10.35378/gujs.776277
Chicago Elgarhy, Mohammed, Amal Soliman, and Heba Nagy. “Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution”. Gazi University Journal of Science 35, no. 2 (June 2022): 731-46. https://doi.org/10.35378/gujs.776277.
EndNote Elgarhy M, Soliman A, Nagy H (June 1, 2022) Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution. Gazi University Journal of Science 35 2 731–746.
IEEE M. Elgarhy, A. Soliman, and H. Nagy, “Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution”, Gazi University Journal of Science, vol. 35, no. 2, pp. 731–746, 2022, doi: 10.35378/gujs.776277.
ISNAD Elgarhy, Mohammed et al. “Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution”. Gazi University Journal of Science 35/2 (June 2022), 731-746. https://doi.org/10.35378/gujs.776277.
JAMA Elgarhy M, Soliman A, Nagy H. Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution. Gazi University Journal of Science. 2022;35:731–746.
MLA Elgarhy, Mohammed et al. “Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution”. Gazi University Journal of Science, vol. 35, no. 2, 2022, pp. 731-46, doi:10.35378/gujs.776277.
Vancouver Elgarhy M, Soliman A, Nagy H. Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution. Gazi University Journal of Science. 2022;35(2):731-46.

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