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Autor
Sabri Shamsul Rijal Muhammad (Universiti Sains Malaysia, Penang, Malaysia), Adetunji Ademola Abiodun (Federal Polytechnic, Ile-Oluji, Nigeria)
Tytuł
On the Poisson-transmuted Exponential Distribution and Its Application to Frequency of Claim in Actuarial Science
Źródło
Statistics in Transition, 2024, vol. 25, nr 2, s. 103-120, tab., wykr., bibliogr. 32 poz.
Słowa kluczowe
Rozkład Poissona, Metoda największej wiarygodności, Estymacja, Modele statystyczne
Poisson distribution, Maximum likelihood estimation, Estimation, Statistical models
Uwagi
summ.
Abstrakt
This study proposes a new discrete distribution in the mixed Poisson paradigm to obtain a distribution that provides a better fit to skewed and dispersed count observation with excess zero. The cubic transmutation map is used to extend the exponential distribution, and the obtained continuous distribution is assumed for the parameter of the Poisson distribution. Various moment-based properties of the new distribution are obtained. The Nelder-Mead algorithm provides the fastest convergence iteration under the maximum likelihood estimation technique. The shapes of the proposed new discrete distribution are similar to those of the mixing distribution. Frequencies of insurance claims from different countries are used to assess the performance of the new proposition (and its zero-inflated form). Results show that the new distribution outperforms other competing ones in most cases. It is also revealed that the natural form of the new distribution outperforms its zeroinflated version in many cases despite having observations with excess zero counts. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka SGH im. Profesora Andrzeja Grodka
Pełny tekst
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Bibliografia
Pokaż
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  5. Al-kadim, K. A., (2018). Proposed Generalized Formula for Transmuted Distribution. Journal of Babylon University, Pure and Applied Sciences, 26(4), pp. 66-74.
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  7. Aslam, M., Hussain, Z., & Asghar, Z., (2018). Cubic Transmuted-G family of distributions and its properties. Stochastic and Quality Control, De Gruyte, 33(2), pp. 103-112. https://doi.org/10.1515/eqc-2017-0027
  8. Bhati, D., Kumawat, P., & Gómez-Déniz, E., (2017). A New Count Model Generated from Mixed Poisson Transmuted Exponential Family with an application to Health Care Data. Communications in Statistics - Theory and Methods, 46(22), pp. 11060- 11076. https://doi.org/10.1080/03610926.2016.1257712
  9. Bhati, D., Sastry, D. V. S., & Maha Qadri, P. Z., (2015). A New Generalized Poisson- Lindley Distribution: Applications and Properties. Austrian Journal of Statistics, 44(4), pp. 35-51. https://doi.org/10.17713/ajs.v44i4.54
  10. Das, K. K., Ahmed, I., & Bhattacharjee, S., (2018). A New Three-Parameter Poisson- Lindley Distribution for Modelling Over-dispersed Count Data. International Journal of Applied Engineering Research, 13(23), pp. 16468-16477. http://www.ripublication.com
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  13. Frees, E. W., (2010). Regression Modeling with Actuarial and Financial Applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511814372
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  15. Gómez-Déniz, E., Calderín-Ojeda, E., (2016). The Poisson-Conjugate Lindley Mixture Distribution. Communications in Statistics - Theory and Methods, 45(10), pp. 2857- 2872. https://doi.org/10.1080/03610926.2014.892134
  16. Granzotto, D. C. T., Louzada, F., & Balakrishnan, N., (2017). Cubic Rank Transmuted Distributions: Inferential Issues and Applications. Journal of Statistical Computation and Simulation, 87(14), pp. 2760-2778. https://doi.org/10.1080/00949655.2017.1344239
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  18. Karlis, D., Xekalaki, E., (2005). Mixed Poisson distributions. International Statistical Review, 73(1), pp. 35-58. https://doi.org/10.1111/j.1751-5823.2005.tb00250.x
  19. Mahdavi, A., Kundu, D., (2017). A new Method for Generating Distributions with an Application to Exponential Distribution. Communications in Statistics - Theory and Methods, 46(13), pp. 6543-6557. https://doi.org/10.1080/03610926. 2015.1130839
  20. Mahmoudi, E., Zakerzadeh, H., (2010). Generalized Poisson-Lindley Distribution. Communications in Statistics - Theory and Methods, 39(10), pp. 1785-1798. https://doi.org/10.1080/03610920902898514
  21. Meytrianti, A., Nurrohmah, S., & Novita, M., (2019). An Alternative Distribution for Modelling Overdispersion Count Data: Poisson Shanker Distribution. ICSA - International Conference on Statistics and Analytics 2019, 1, pp. 108-120. https://doi.org/10.29244/icsa.2019.pp108-120
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  23. Nikoloulopoulos, A. K., & Karlis, D., (2008). On modeling count data: A comparison of some well-known discrete distributions. Journal of Statistical Computation and Simulation, 78(3), pp. 437-457. https://doi.org/10.1080/10629360601010760
  24. Omari, C. O., Nyambura, S. G., & Mwangi, J. M. W., (2018). Modeling the Frequency and Severity of Auto Insurance Claims Using Statistical Distributions. Journal of Mathematical Finance, 8(1), pp. 137-160. https://doi.org/10.4236/jmf.2018.81012
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  26. Rahman, M. M., Al-Zahrani, B., Shahbaz, S. H., & Shahbaz, M. Q., (2019). Cubic Transmuted Uniform Distribution: An Alternative to Beta and Kumaraswamy Distributions. European Journal of Pure and Applied Mathematics, 12(3), 1106- 1121. https://doi.org/10.29020/nybg.ejpam.v12i3.3410
  27. Rasekhi, M., Alizadeh, M., Altun, E., Hamedani, G., Afify, A. Z., & Ahmad, M., (2017). The Modified Exponential Distribution with Applications. Pakistan Journal of Statistics, 33(5), pp. 383-398.
  28. Shaw, W. T., Buckley, I. R. C., (2007). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report.
  29. Shehata, W. A. M., Yousof, H., & 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), pp. 943-961. https://doi.org/10.18187/pjsor.v17i4.3903
  30. Yang, Y., Tian, W., & Tong, T., (2021). Generalized Mixtures of Exponential Distribution and Associated Inference. Mathematics, 9(12), pp. 1-22. https://doi.org/10.3390/math9121371
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  32. Zamani, H., Ismail, N., (2014). Functional form for the Zero Inflated Generalized Poisson Regression Model. Communications in Statistics - Theory and Methods, 43, pp. 515-529.
Cytowane przez
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ISSN
1234-7655
Język
eng
URI / DOI
http://dx.doi.org/10.59170/stattrans-2024-017
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