IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v54y2014icp49-57.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713001716
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2013.10.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    3. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    4. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    5. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    6. Gordy, Michael B, 1998. "Computationally Convenient Distributional Assumptions for Common-Value Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 12(1), pages 61-78, August.
    7. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
    8. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
    9. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    10. Serhan Ziya & Hayriye Ayhan & Robert D. Foley, 2004. "Relationships Among Three Assumptions in Revenue Management," Operations Research, INFORMS, vol. 52(5), pages 804-809, October.
    11. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.
    16. Shovan Chowdhury & Amarjit Kundu, 2016. "Stochastic Comparison of Parallel Systems with Finite Range Distributed Components," Working papers 201, Indian Institute of Management Kozhikode.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Chaves, Isaías N. & Ichihashi, Shota, 2024. "Auction timing and market thickness," Games and Economic Behavior, Elsevier, vol. 143(C), pages 161-178.
    3. Schweizer, Nikolaus & Szech, Nora, 2015. "The quantitative view of Myerson regularity," Discussion Papers, Research Unit: Economics of Change SP II 2015-307, WZB Berlin Social Science Center.
    4. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    5. Liu, Tian-Liang & Chen, Jian & Huang, Hai-Jun, 2011. "Existence and efficiency of oligopoly equilibrium under toll and capacity competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 908-919.
    6. Maha A. Omair & Yusra A. Tashkandy & Sameh Askar & Abdulhamid A. Alzaid, 2022. "Family of Distributions Derived from Whittaker Function," Mathematics, MDPI, vol. 10(7), pages 1-23, March.
    7. Brusset, Xavier & Cattan-Jallet, Roxane, 2009. "Estimating the buyer's willingness to pay using Bayesian belief distribution with IFR," MPRA Paper 22638, University Library of Munich, Germany, revised 10 May 2010.
    8. Ayşe Kocabıyıkoğlu & Ioana Popescu, 2011. "An Elasticity Approach to the Newsvendor with Price-Sensitive Demand," Operations Research, INFORMS, vol. 59(2), pages 301-312, April.
    9. Colombo, Luca & Labrecciosa, Paola, 2012. "A note on pricing with risk aversion," European Journal of Operational Research, Elsevier, vol. 216(1), pages 252-254.
    10. Shovan Chowdhury & Amarjit Kundu, 2016. "Stochastic Comparison of Parallel Systems with Finite Range Distributed Components," Working papers 201, Indian Institute of Management Kozhikode.
    11. Xu, Xiaolin & Cai, Xiaoqiang & Chen, Youhua, 2011. "Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications," International Journal of Production Economics, Elsevier, vol. 133(2), pages 653-661, October.
    12. 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.
    13. Xiaoming Yan & Yong Wang & Zhaofu Hong, 2016. "Comparison of Bertrand and Cournot competitions under random yield," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3256-3276, June.
    14. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    15. Emilio Gómez-Déniz & José María Sarabia, 2018. "A Family of Generalised Beta Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 5(3), pages 401-420, September.
    16. Anh Ninh & Zuo‐Jun Max Shen & Martin A. Lariviere, 2020. "Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 788-796, March.
    17. Hurairah Ahmed & Alabid Abdelhakim, 2020. "Beta transmuted Lomax distribution with applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 13-34, June.
    18. Karimi, Majid & Zaerpour, Nima, 2022. "Put your money where your forecast is: Supply chain collaborative forecasting with cost-function-based prediction markets," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1035-1049.
    19. Yunzeng Wang, 2006. "Joint Pricing-Production Decisions in Supply Chains of Complementary Products with Uncertain Demand," Operations Research, INFORMS, vol. 54(6), pages 1110-1127, December.
    20. Zelong Yi & Yulan Wang & Ying‐Ju Chen, 2021. "Financing an Agricultural Supply Chain with a Capital‐Constrained Smallholder Farmer in Developing Economies," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2102-2121, July.
    21. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:54:y:2014:i:c:p:49-57. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.