Main Article Content

Abstract

In this work, we construct a three-parameter Chen modification that is flexible. The "J shape", "monotonically increasing", "U shape," and "upside down (reversed bathtub)" hazard rate forms are all supported by the new Chen extension's hazard rate. We derive pertinent statistical features. A few distributions of the bivariate kind are generated. For evaluating the model parameters, we took the maximum likelihood estimation approach into consideration. Maximal likelihood estimators are evaluated via graphical simulations. To demonstrate the applicability of the new approach, two genuine data sets are taken into consideration and examined. The Akaike Information criterion, Bayesian Information criterion, Cramer-von Mises criterion, Anderson-Darling criterion, Kolmogorov-Smirnov test, and its related p-value are used to evaluate the new model with a variety of popular competing models.

Keywords

Chen Distribution Maximum Likelihood Simulations; Hazard Rate Farlie-Gumbel-Morgenstern Copula Clayton Copula

Article Details

Author Biography

Emadeldin I. A. Ali, Department of Economics, College of Economics and Administrative Sciences, Al Imam Mohammad Ibn Saud Islamic University, Saudi Arabia

Department of Mathematics, Statistics, and Insurance, Faculty of Business, Ain Shams University, Egypt; Email: i_emadeldin@yahoo.com

How to Cite
Refaie, M. K. A., Butt, N. S., & Ali, E. I. A. (2023). A new probability distribution: properties, copulas and applications in medicine and engineering. Pakistan Journal of Statistics and Operation Research, 19(2), 257-278. https://doi.org/10.18187/pjsor.v19i2.3633

References

  1. Ali, M. M., Ibrahim, M. and Yousof, H. M. (2022). A New Flexible Three-Parameter Compound Chen Distribution: Properties, Copula and Modeling Relief Times and Minimum Flow Data. Bulletin of the Malaysian Mathematical Sciences Society, 45(1), 130-160.
  2. Alzaatreh, A., Famoye, F. and Lee, C. (2014). The gamma-normal distribution: Properties and applications. Computational Statistics and Data Analysis, 69, 67-80.
  3. Balakrishnan, N., Cohen, A. C. (2014). Order Statistics & Inference: Estimation Methods. Academic Press, London: Elsevier.
  4. Chaubey, Y. P., Zhang, R. (2015). An extension of Chen's family of survival distributions with bathtub shape or increasing hazard rate function. Communications in Statistics-Theory and Methods 44(19), 4049--4064.
  5. Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters 49(2), 155--161.
  6. Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-893.
  7. Dey, S., Kumar, D., Ramos, P. L. and Louzada, F. (2017). Exponentiated Chen distribution: Properties and estimation. Communications in Statistics-Simulation and Computation, 46(10), 8118-8139.
  8. Elgohari, H. and Yousof, H. M. (2020a). A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications. Pakistan Journal of Statistics and Operation Research, 16(4), 697-711. https://doi.org/10.18187/pjsor.v16i4.3260
  9. Elgohari, H. and Yousof, H. M. (2021b). A New Extreme Value Model with Different Copula, Statistical Properties and Applications. Pakistan Journal of Statistics and Operation Research, 17(4), 1015-1035. https://doi.org/10.18187/pjsor.v17i4.3471
  10. Elgohari, H. and Yousof, H. M. (2020c). New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling. Statistics, Optimization & Information Computing, 8(4), 972-993. https://doi.org/10.19139/soic-2310-5070-1036
  11. Elgohari, H., Ibrahim, M. and Yousof, H. M. (2021). A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods. Statistics, Optimization & Information Computing, 8(3), 555-586.
  12. Emam, W.; Tashkandy, Y.; Goual, H.; Hamida, T.; Hiba, A.; Ali, M.M.; Yousof, H.M.; Ibrahim, M. A New One-Parameter Distribution for Right Censored Bayesian and Non-Bayesian Distributional Validation under Various Estimation Methods. Mathematics 2023a, 11, 897. https://doi.org/10.3390/math11040897
  13. Emam, W.; Tashkandy, Y.; Hamedani, G.G.; Shehab, M.A.; Ibrahim, M.; Yousof, H.M. A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero‐Inflated Real Data with Bayesian, and Non‐Bayesian Inference. Mathematics 2023b, 11, 1125. https://doi.org/10.3390/math11051125
  14. Eugene, N., Lee, C., and Famoye, F. (2002). Beta-Normal distribution and its Applications. Communications in Statistics -Theory and Methods, 31, 497-512.
  15. Farlie, D. J. G. (1960) The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 47, 307-323.
  16. Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56(294), 335-349.
  17. Gumbel, E. J. (1960) Bivariate exponential distributions. Journ. Amer. Statist. Assoc., 55, 698-707.
  18. Ibrahim, M., Aidi, K., Ali, M. M. and Yousof, H. M. (2022). A Novel Test Statistic for Right Censored Validity under a new Chen extension with Applications in Reliability and Medicine. Annals of Data Science, forthcoming. doi.org/10.1007/s40745-022-00416-6
  19. Ibrahim, M.; Emam, W.; Tashkandy, Y.; Ali, M.M.; Yousof, H.M. Bayesian and Non-Bayesian Risk Analysis and Assessment under Left-Skewed Insurance Data and a Novel Compound Reciprocal Rayleigh Extension. Mathematics 2023, 11, 1593. https://doi.org/10.3390/ math11071593
  20. Johnson, N. L. and Kotz, S. (1975) On some generalized Farlie-Gumbel-Morgenstern distributions. Commun. Stat. Theory, 4, 415-427.
  21. Johnson, N. L. and Kotz, S. (1977) On some generalized Farlie-Gumbel-Morgenstern distributions- II: Regression, correlation and further generalizations. Commun. Stat.Theory, 6, 485-496.
  22. Johnson, N. L., Kemp, A. W. and Kotz, S. (2005). Univariate discrete distributions, 3rd edn. Wiley, Hoboken.
  23. Jose, K. K. (2011). Marshall-Olkin family of distributions and their applications in reliability theory, time series modeling and stress-strength analysis. Proc. ISI 58th World Statist. Congr Int Stat Inst, 21st-26th August, 3918-3923.
  24. Khan, M. S., King, R. and Hudson, I. L. (2013). A new three parameter transmuted Chen lifetime distribution with application. Journal of Applied Statistical Science, 21, 239-259.
  25. Khan, M. S., King, R. and Hudson, I. L. (2016). Transmuted exponentiated Chen distribution with application to survival data. ANZIAM Journal, 57, 268-290.
  26. Korkmaz, M. Ç., Altun, E., Chesneau, C. and Yousof, H. M. (2022). On the unit-Chen distribution with associated quantile regression and applications. Mathematica Slovaca, 72 (2022), No. 3, 765-786.
  27. Mohamed, H. S., Ali, M. M. and Yousof, H. M. (2022a). The Lindley Gompertz Model for Estimating the Survival Rates: Properties and Applications in Insurance, Annals of Data Science, 10.1007/s40745-022-00451-3
  28. Mohamed, H. S., Cordeiro, G. M. and Yousof, H. M. (2022b). The synthetic autoregressive model for the insurance claims payment data: modeling and future prediction. Statistics, Optimization & Information Computing, forthcoming.
  29. Mohamed, H. S., Cordeiro, G. M., Minkah, R., Yousof, H. M. and Ibrahim, M. (2022c). A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting. Journal of Applied Statistics, forthcoming.
  30. Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt fur Mathematische Statistik, 8, 234-235.
  31. Pougaza, D. B. and Djafari, M. A. (2011). Maximum entropies copulas. Proceedings of the 30th international workshop on Bayesian inference and maximum Entropy methods in Science and Engineering, 329-336.
  32. Rodriguez-Lallena, J. A. and Ubeda-Flores, M. (2004). A new class of bivariate copulas. Statistics and Probability Letters, 66, 315--25.
  33. 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.
  34. Shehata, W. A. M. and Yousof, H. M. (2021). The four-parameter exponentiated Weibull model with Copula, properties and real data modeling. Pakistan Journal of Statistics and Operation Research, 17(3), 649-667.
  35. Shehata, W. A. M., Yousof, H. M., & Aboraya, M. (2021). A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas . Pakistan Journal of Statistics and Operation Research, 17(4), 943-961. https://doi.org/10.18187/pjsor.v17i4.3903
  36. Shehata, W. A. M., Butt, N. S., Yousof, H., & Aboraya, M. (2022). A New Lifetime Parametric Model for the Survival and Relief Times with Copulas and Properties. Pakistan Journal of Statistics and Operation Research, 18(1), 249-272.
  37. Yousof, H., Afify, A., Hamedani, G. G., and Aryal, G. (2017). The Burr X Generator of Distributions for Lifetime Data. Journal of Statistical Theory and Applications, 16: 288-305.
  38. Yousof, H. M., Emam, W., Tashkandy, Y., Ali, M. M., Minkah, R. and Ibrahim, M. (2023). A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling. Mathematics, 11, 1284. https://doi.org/10.3390/math11061284
  39. Yousof, H. M., Korkmaz, M. Ç., 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.

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