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Estimation of the Density and Cumulative Distribution Functions of the Topp-Leone Distribution

Year 2023, Volume: 44 Issue: 3, 610 - 616, 29.09.2023

Lazhar Benkhelıfa

https://doi.org/10.17776/csj.1180040

Abstract

In this paper, we estimate the probability density function and the cumulative distribution function of the Topp-Leone distribution. We use the maximum likelihood estimation, uniformly minimum variance unbiased estimation, least squares estimation, weighted least squares estimation, Cramér-von Mises estimation, Anderson-Darling estimation and method of percentile estimation. The consistency of these methods is illustrated in a simulation study. Finally, a real data set is given to assess the performance of proposed methods.

Keywords

Topp-Leone distribution Maximum likelihood least squares estimation Weighted least squares estimation Cramér-von Mises estimation Anderson-Darling estimation.

References

  • [1] Akgül F. G., Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution, J. Stat. Comput. Simul, 89 (2019) 2914-2929.
  • [2] Alizadeh M., Bagheri S.F., Baloui Jamkhaneh E., Nadarajah, S., Estimates of the PDF and the CDF of the exponentiated Weibull distribution, Braz. J. Probab. Stat., 29 (2015) 695-716.
  • [3] Bagheri S.F., Alizadeh M., Baloui Jamkhaneh E., Nadarajah S., Evaluation and comparison of estimations in the generalized exponential-Poisson distribution, J. Stat. Comput. Simul., 84 (2014) 2345-2360.
  • [4] Bagheri S. F., Alizadeh M., Nadarajah S., Deiri E., Efficient estimation of the PDF and the CDF of the weibull extension model, Commun. Stat. Simul. Comput., 45 (2016) 2191-2207.
  • [5] Bayoud H.A., Admissible minimax estimators for the shape parameter of Topp-Leone distribution, Comm. Statist. Theory Methods, 45 (2016) 71-82.
  • [6] Benkhelifa L., Alpha power Topp-Leone Weibull distribution: Properties, Characterizations, Regression modeling and applications, J. Stat. Manag. Systs., 25 (2022) 1945-1970.
  • [7] Dixit U.J., Jabbari Nooghabi M., Efficient estimation in the Pareto distribution, Stat. Methodol., 7 (2010) 687-691.
  • [8] Genç A.İ., Moments of order statistics of Topp-Leone distribution, Statist. Papers, 53 (2012) 117-131.
  • [9] Genç A.İ., Estimation of P(X>Y) with Topp-Leone distribution, J. Stat. Comput. Simul., 83 (2012) 326-339.
  • [10] Ghitany M.E., Kotz S., Xie M., On some reliability measures and their stochastic orderings for the Topp-Leone distribution, J. Appl. Stat., 32 (2005) 715-722.
  • [11] Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products. Sixth ed. Academic Press, San Diego, (2000).
  • [12] Hassan A. S., Assar S. M., Ali K. A., Nagy H. F., Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution, Stat. Transit, 22 (2021) 171-189.
  • [13] Kao J.H.K., Computer methods for estimating Weibull parameters in reliability studies, Trans. IRE-Reliab. Qual. Control., 13 (1958) 15-22.
  • [14] Kao J.H.K., A graphical estimation of mixed Weibull parameters in life testing electron tubes, Technometrics, 1 (1959) 389-407.
  • [15] Long B., Estimation and prediction for Topp--Leone distribution using double Type-I hybrid censored data, J. Stat. Comput. Simul., 92 (2022) 2999-3019.
  • [16] Maiti S. S., Mukherjee I., On estimation of the PDF and CDF of the Lindley distribution, Commun. Stat. Simul. Comput., 47 (2018) 1370-1381.
  • [17] Maleki Jebely F., Zare K., Deiri E., Efficient estimation of the PDF and the CDF of the inverse Rayleigh distribution, J. Stat. Comput. Simul., 88 (2018) 75-88.
  • [18] Nadarajah S., Kotz S., Moments of some J-shaped distributions, J. Appl. Stat., 30 (2003) 311-317.
  • [19] Suprawhardana M.S., Prayoto S., Total time on test plot analysis for mechanical components of the RSG-GAS reactor, Atom Indones, 25 (1999) 81-90.
  • [20] Saini S., Tomer S., Garg R., Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data, J. Appl. Statist., (2022)
  • [21] Swain J., Venkatraman S., Wilson J., Least squares estimation of distribution functions in Johnson's translation system, J. Stat. Comput. Simul., 29 (1988) 271-297.
  • [22] Topp C.W., Leone F.C., A family of J-shaped frequency functions, J. Amer. Statist. Assoc., 50 (1955) 209-219.
  • [23] Vicari D., Van Dorp J.R., Kotz S., Two-sided generalized Topp and Leone (TS-GTL) distributions, J. Appl. Statist., 35 (2008) 1115-1129.

Year 2023, Volume: 44 Issue: 3, 610 - 616, 29.09.2023

Lazhar Benkhelıfa

https://doi.org/10.17776/csj.1180040

Abstract

References

  • [1] Akgül F. G., Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution, J. Stat. Comput. Simul, 89 (2019) 2914-2929.
  • [2] Alizadeh M., Bagheri S.F., Baloui Jamkhaneh E., Nadarajah, S., Estimates of the PDF and the CDF of the exponentiated Weibull distribution, Braz. J. Probab. Stat., 29 (2015) 695-716.
  • [3] Bagheri S.F., Alizadeh M., Baloui Jamkhaneh E., Nadarajah S., Evaluation and comparison of estimations in the generalized exponential-Poisson distribution, J. Stat. Comput. Simul., 84 (2014) 2345-2360.
  • [4] Bagheri S. F., Alizadeh M., Nadarajah S., Deiri E., Efficient estimation of the PDF and the CDF of the weibull extension model, Commun. Stat. Simul. Comput., 45 (2016) 2191-2207.
  • [5] Bayoud H.A., Admissible minimax estimators for the shape parameter of Topp-Leone distribution, Comm. Statist. Theory Methods, 45 (2016) 71-82.
  • [6] Benkhelifa L., Alpha power Topp-Leone Weibull distribution: Properties, Characterizations, Regression modeling and applications, J. Stat. Manag. Systs., 25 (2022) 1945-1970.
  • [7] Dixit U.J., Jabbari Nooghabi M., Efficient estimation in the Pareto distribution, Stat. Methodol., 7 (2010) 687-691.
  • [8] Genç A.İ., Moments of order statistics of Topp-Leone distribution, Statist. Papers, 53 (2012) 117-131.
  • [9] Genç A.İ., Estimation of P(X>Y) with Topp-Leone distribution, J. Stat. Comput. Simul., 83 (2012) 326-339.
  • [10] Ghitany M.E., Kotz S., Xie M., On some reliability measures and their stochastic orderings for the Topp-Leone distribution, J. Appl. Stat., 32 (2005) 715-722.
  • [11] Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products. Sixth ed. Academic Press, San Diego, (2000).
  • [12] Hassan A. S., Assar S. M., Ali K. A., Nagy H. F., Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution, Stat. Transit, 22 (2021) 171-189.
  • [13] Kao J.H.K., Computer methods for estimating Weibull parameters in reliability studies, Trans. IRE-Reliab. Qual. Control., 13 (1958) 15-22.
  • [14] Kao J.H.K., A graphical estimation of mixed Weibull parameters in life testing electron tubes, Technometrics, 1 (1959) 389-407.
  • [15] Long B., Estimation and prediction for Topp--Leone distribution using double Type-I hybrid censored data, J. Stat. Comput. Simul., 92 (2022) 2999-3019.
  • [16] Maiti S. S., Mukherjee I., On estimation of the PDF and CDF of the Lindley distribution, Commun. Stat. Simul. Comput., 47 (2018) 1370-1381.
  • [17] Maleki Jebely F., Zare K., Deiri E., Efficient estimation of the PDF and the CDF of the inverse Rayleigh distribution, J. Stat. Comput. Simul., 88 (2018) 75-88.
  • [18] Nadarajah S., Kotz S., Moments of some J-shaped distributions, J. Appl. Stat., 30 (2003) 311-317.
  • [19] Suprawhardana M.S., Prayoto S., Total time on test plot analysis for mechanical components of the RSG-GAS reactor, Atom Indones, 25 (1999) 81-90.
  • [20] Saini S., Tomer S., Garg R., Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data, J. Appl. Statist., (2022)
  • [21] Swain J., Venkatraman S., Wilson J., Least squares estimation of distribution functions in Johnson's translation system, J. Stat. Comput. Simul., 29 (1988) 271-297.
  • [22] Topp C.W., Leone F.C., A family of J-shaped frequency functions, J. Amer. Statist. Assoc., 50 (1955) 209-219.
  • [23] Vicari D., Van Dorp J.R., Kotz S., Two-sided generalized Topp and Leone (TS-GTL) distributions, J. Appl. Statist., 35 (2008) 1115-1129.
There are 23 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Lazhar Benkhelıfa 0000-0002-7271-418X

Publication Date September 29, 2023
Submission Date September 25, 2022
Acceptance Date September 5, 2023
Published in Issue Year 2023Volume: 44 Issue: 3

Cite

APA Benkhelıfa, L. (2023). Estimation of the Density and Cumulative Distribution Functions of the Topp-Leone Distribution. Cumhuriyet Science Journal, 44(3), 610-616. https://doi.org/10.17776/csj.1180040
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