On Truncated Versions of Xgamma Distribution: Various Estimation Methods and Statistical modelling

  • Subhradev Sen
  • Morad Alizadeh
  • Mohamed Aboraya
  • M. Masoom Ali
  • Haitham M. Yousof
  • Mohamed Ibrahim Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt
Keywords: lifetime distribution, truncated distribution, survival, maximum likelihood, order statistics

Abstract

In this article, we introduced the truncated versions (lower, upper and double) of xgamma distribution (Sen et al. 2016). In particular, different structural and distributional properties such as moments, popular entropy measures, order statistics and survival characteristics of the upper truncated xgamma distribution are discussed in detail. We briefly describe different estimation methods, namely the maximum likelihood, ordinary least squares, weighted least square and L-Moments. Monte Carlo simulation experiments are performed for comparing the performances of the proposed methods of estimation for both small and large samples under the lower, upper and double versions. Two applications are provided, the first one comparing estimationmethods and the other for illustrating the applicability of the new model.

References

Aboraya, M., Ali, M. M., Yousof, H. M. and Ibrahim, M. (2022). A Novel Lomax Extension with Statistical Properties,

Copulas, Different Estimation Methods and Applications. Bulletin of the Malaysian Mathematical Sciences Society, (2022)

https://doi.org/10.1007/s40840-022-01250-y

Aboraya, M., M. Yousof, H. M., Hamedani, G. G. and Ibrahim, M. (2020). A new family of discrete distributions with mathematical properties, characterizations, Bayesian and non-Bayesian estimation methods. Mathematics, 8, 1648.

Ali, M. M., Ali, I., Yousof, H. M. and Ibrahim, M. (2022). G Families of Probability Distributions: Theory and Practices. CRC Press, Taylor & Francis Group.

Cho, B. R. and Govindaluri, M. S. (2002). Optimal screening limits in multi-stage assemblies. International journal of production research, 40(9), 1993-2009.

Cordeiro, G. M., Altun, E., Korkmaz, M. C., Pescim, R. R. and Afify, A. Z. and Yousof, H. M. (2020). The xgamma Family: Censored Regression Modelling and Applications. Revstat Statistical Journal, 18(5), 593–612.

Elgohari, H., Ibrahim, M. and Yousof, H. M. (2021d). A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods. Statistics, Optimization & Information Computing, 8(3), 555-586.

Eliwa, M. S., El-Morshedy, M. and Yousof, H. M. (2022). A Discrete Exponential Generalized-G Family of Distributions:

Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data. Mathematics, 10, 3348. https://doi.org/10.3390/math10183348

El-Morshedy, M., Eliwa, M. S., Al-Bossly, A. and Yousof, H. M. (2022). A New Probability Heavy-Tail Model for Stochastic

Modeling under Engineering Data. Journal of Mathematics, 2022, 1-20, https://doi.org/10.1155/2022/1910909

Gupta, R. (2001). System and Bayesian Reliability: Essays in Honour of Professor R.E Barlow. Series on Quality, Reliability and Engineering Statistics, chap. Nonmonotonic failure rates and mean residual life functions, World Scientfic Press, Singapore, 147-163.

Field, T., Harder, U. and Harrison, P. (2004). Network traffic behaviour in switched Ethernet systems. Performance Evaluation, 58(2), 243-260.

Fuller Jr, E. R., Freiman, S. W., Quinn, J. B., Quinn, G. D. and Carter, W. C. (1994). Fracture mechanics approach to the design of glass aircraft windows: a case study. In SPIE’s 1994 International Symposium on Optics, Imaging and Instrumentation, 419-430.

Hamed, M. S., Cordeiro, G. M. and Yousof, H. M. (2022). A New Compound Lomax Model: Properties, Copulas, Modeling and Risk Analysis Utilizing the Negatively Skewed Insurance Claims Data. Pakistan Journal of Statistics and Operation Research, 18(3), 601-631. https://doi.org/10.18187/pjsor.v18i3.3652

Hamedani, G. G., Korkmaz, M. C., Butt, N. S. and Yousof, H. M. (2021). The Type I Quasi Lambert Family: Properties,

Characterizations and Different Estimation Methods. Pakistan Journal of Statistics and Operation Research, 17(3), 545-558.

Hegde, L. M. and Dahiya, R. C. (1989). Estimation of the parameters of a truncated gamma distribution. Communications in StatisticsTheory and Methods, 18(2), 561-577.

Ibrahim. M., Aidi, K., Ali, M. M. and Yousof, H. M. (2021). The Exponential Generalized Log-Logistic Model: BagdonaviˇciusNikulin test for Validation and Non-Bayesian Estimation Methods. Communications for Statistical Applications and Methods, 29(1), 681–705.

Ibrahim, M., Ali, M. M. and Yousof, H. M. (2021). The discrete analogue of the Weibull G family: properties, different applications, Bayesian and non-Bayesian estimation methods. Annals of Data Science, forthcoming.

Ibrahim, M., Altun, E. and Yousof, H. M. (2020). A new distribution for modeling lifetime data with different methods of estimation and censored regression modeling. Statistics, Optimization & Information Computing, 8(2), 610-630.

Ibrahim, M., Altun, E., Goual, H., and Yousof, H. M. (2020). Modified goodness-of-fit type test for censored validation under a new Burr type XII distribution with different methods of estimation and regression modeling. Eurasian Bulletin of Mathematics, 3(3), 162-182.

Ibrahim, M., Hamedani, G. G., Butt, N. S. and Yousof, H. M. (2022). Expanding the Nadarajah Haghighi Model: Copula, Censored and Uncensored Validation, Characterizations and Applications. Pakistan Journal of Statistics and Operation Research, 18(3), 537-553. https://doi.org/10.18187/pjsor.v18i3.3420

Ibrahim. M., Handique, L., Chakraborty, S., Butt, N. S. and M. Yousof, H. (2021). A new three-parameter xgamma Fr´echet distribution with different methods of estimation and applications. Pakistan Journal of Statistics and Operation Research, 17(1), 291-308.

Ibrahim, M., Yadav, A. S., Yousof, H. M., Goual, H. and Hamedani, G. G. (2019). A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation. Communications for Statistical Applications and Methods, 26(5), 473-495.

Kapur, K. C. and Cho, B. R. (1994). Economic design and development of specifications. Quality Engineering, 6(3), 401-417.

Kapur, K. C. and Cho, B. R. (1996). Economic design of the specification region for multiple quality characteristics. IIE transactions, 28(3), 237-248.

Khasawneh, M. T., Bowling, S. R., Kaewkuekool, S. and Cho, B. R. (2004). Tables of a truncated standard normal distribution: A singly truncated case. Quality Engineering, 17(1), 33-50.

Khasawneh, M. T., Bowling, S. R., Kaewkuekool, S. and Cho, B. R. (2005). Tables of a truncated standard normal distribution: a doubly truncated case. Quality Engineering, 17(2), 227-241.

Mansour, M., Rasekhi, M., Ibrahim, M., Aidi, K., Yousof, H. M. and Elrazik, E. A. (2020). A New Parametric Life Distribution with Modified Bagdonaviˇcius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods. Entropy, 22(5), 592.

Mansour, M., Yousof, H. M., Shehata, W. A. M. and Ibrahim, M. (2020). A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data. Journal of Nonlinear Science and Applications, 13(5), 223-238.

Mittal, M. M. and Dahiya, R. C. (1989). Estimating the parameters of a truncated Weibull distribution. Communications in StatisticsTheory and Methods, 18(6), 2027-2042.

Mukhopadhyay, A., Bhowmick, K. and Mitra, G. B. (2000). Edgeworth series expansion of the truncated Cauchy function and its effectiveness in the study of atomic heterogeneity. Zeitschrift f¨ur Kristallographie-Crystalline Materials, 215(12), 718-726.

Nadarajah, S. (2008). A truncated inverted beta distribution with application to air pollution data. Stochastic Environmental Research and Risk Assessment, 22(2), 285-289.

Phillips, M. D. and Cho, B. R. (1998). Quality improvement for processes with circular and spherical specification regions. Quality Engineering, 11(2), 235-243.

Phillips, M. D. and Cho, B. R. (2000). Modelling of optimal specification regions. Applied Mathematical Modelling, 24(5), 327-341.

Salah, M. M., El-Morshedy, M., Eliwa, M. S. and Yousof, H. M. (2020). Expanded Fr´echet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing. Mathematics, 8(11), 1949.

Sen, S., Korkmaz, M. C. and Yousof, H. M. (2018). The quasi xgamma-Poisson distribution. ISTATISTIK: JOURNAL OF THE TURKISH STATISTICAL ASSOCIATION, 11(3), 65-76.

Sen, S., Maiti, S. S. and Chandra, N. (2016). The xgamma Distribution: Statistical Properties and Application. Journal of Modern Applied Statistical Methods, 15(1), 774-788.

Shehata, W. A. M. and Yousof, H. M. (2022). A novel two-parameter Nadarajah-Haghighi extension: properties, copulas, modeling real data and different estimation methods. Statistics, Optimization & Information Computing, 10(3), 725-749.

Yadav, A. S., Goual, H., Alotaibi, R. M., Rezk, H., Ali, M. M. and Yousof, H. M. (2020). Validation of the Topp-Leone-Lomax model via a modified Nikulin-Rao-Robson goodness-of-fit test with different methods of estimation. Symmetry, 12(1), 57.

Yousof, H. M., Ali, M. M., Goual, H. and Ibrahim. M. (2021). A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and modified right censored test for validation, Statistics in Transition New Series, 23(3), 1-23.

Yousof, H. M., Ali, M. M., Hamedani, G. G., Aidi, K. & Ibrahim, M. (2022). A new lifetime distribution with properties,

characterizations, validation testing, different estimation methods. Statistics, Optimization & Information Computing, 10(2), 519-547.

Yousof, H. M., Hamedani, G. G. and Ibrahim, M. (2020). The Two-parameter Xgamma Fr´echet Distribution: Characterizations, Copulas, Mathematical Properties and Different Classical Estimation Methods. Contributions to Mathematics, 2 (2020), 32-41.

Yousof, H. M., Korkmaz, M. C¸ ., K., Hamedani, G. G and Ibrahim, M. (2022). A novel Chen extension: theory, characterizations and different estimation methods. Eur. J. Stat, 2(2022), 1-20.

Tsallis, C. (1988). Possible generalization of boltzmann-gibbs statistics. Journal of statistical physics, 52(1-2), 479-487.

Zaninetti, L. and Ferraro, M. (2008). On the truncated Pareto distribution with applications. Open Physics, 6(1), 1-6.

Zhang, T. and Xie, M. (2011). On the upper truncated Weibull distribution and its reliability implications. Reliability Engineering & System Safety, 96(1), 194-200.

Published
2023-12-19
How to Cite
Sen, S., Alizadeh, M., Mohamed Aboraya, Ali, M. M., M. Yousof, H., & Mohamed Ibrahim. (2023). On Truncated Versions of Xgamma Distribution: Various Estimation Methods and Statistical modelling. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-1660
Section
Research Articles

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