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The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance

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  • Gómez-Déniz, Emilio
  • Sordo, Miguel A.
  • Calderín-Ojeda, Enrique

Abstract

In this paper a new probability density function with bounded domain is presented. The new distribution arises from the generalized Lindley distribution proposed by Zakerzadeh and Dolati (2010). This new distribution that depends on two parameters can be considered as an alternative to the classical beta distribution. It presents the advantage of not including any special function in its formulation. After studying its most important properties, some useful results regarding insurance and inventory management applications are obtained. In particular, in insurance, we suggest a special class of distorted premium principles based on this distribution and we compare it with the well-known power dual premium principle. Since the mean of the new distribution can be normalized to give a simple parameter, this new model is appropriate to be used as a regression model when the response is bounded, being therefore an alternative to the beta regression model recently proposed in the statistical literature.

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  • Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
    • Handle: RePEc:eee:insuma:v:54:y:2014:i:c:p:49-57
    DOI: 10.1016/j.insmatheco.2013.10.017
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    1. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    2. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    3. Wang, Shaochen & Weiß, Christian H., 2023. "New characterizations of the (discrete) Lindley distribution and their applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 310-322.
    4. Jodrá, P. & Jiménez-Gamero, M.D., 2016. "A note on the Log-Lindley distribution," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 189-194.
    5. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    6. Emrah Altun & Gauss M. Cordeiro, 2020. "The unit-improved second-degree Lindley distribution: inference and regression modeling," Computational Statistics, Springer, vol. 35(1), pages 259-279, March.
    7. Tomaz Ponce Dentinho, 2017. "Urban Concentration and Spatial Allocation of Rents from natural resources. A Zipf's Curve Approach," REGION, European Regional Science Association, vol. 4, pages 77-86.
    8. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.
    9. Tomaz Ponce DENTINHO & Cristina SERBANICA, 2020. "Space justice, demographic resilience and sustainability. Revelations of the evolution of the population hierarchy of the regions of Romania from 1948 to 2011," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 11, pages 27-44, June.
    10. Ghosh Indranil & Dey Sanku & Kumar Devendra, 2019. "Bounded M-O Extended Exponential Distribution with Applications," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 35-51, June.
    11. Valiollahi, R. & Raqab, Mohammad Z. & Asgharzadeh, A. & Alqallaf, F.A., 2018. "Estimation and prediction for power Lindley distribution under progressively type II right censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 32-47.
    12. Ahmed M. T. Abd El-Bar & Willams B. F. da Silva & Abraão D. C. Nascimento, 2021. "An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data," Mathematics, MDPI, vol. 9(23), pages 1-15, December.
    13. Shovan Chowdhury & Asok K Nanda, 2015. "A special class of distorted premium principle based on an extension of the exponential-geometric distribution," Working papers 188, Indian Institute of Management Kozhikode.
    14. Terezinha K. A. Ribeiro & Silvia L. P. Ferrari, 2023. "Robust estimation in beta regression via maximum L $$_q$$ q -likelihood," Statistical Papers, Springer, vol. 64(1), pages 321-353, February.
    15. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2021. "Theory and Applications of the Unit Gamma/Gompertz Distribution," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
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    17. Jiaxin Nie & Wenhao Gui, 2019. "Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals," Mathematics, MDPI, vol. 7(7), pages 1-15, July.

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