IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2022y2022i1n4288286.html

A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications

Author

Listed:
  • Ayed R. A. Alanzi
  • M. Qaisar Rafique
  • M. H. Tahir
  • Waqas Sami
  • Farrukh Jamal

Abstract

In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well‐established actuarial measures such as value‐at‐risk, expected‐shortfall, tail‐value‐at‐risk, tail‐variance, and tail‐variance‐premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real‐life data sets are considered to prove this claim.

Suggested Citation

  • Ayed R. A. Alanzi & M. Qaisar Rafique & M. H. Tahir & Waqas Sami & Farrukh Jamal, 2022. "A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4288286
    DOI: 10.1155/2022/4288286
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/4288286
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/4288286?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    3. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    4. Ahmed Z. Afify & Ahmed M. Gemeay & Noor Akma Ibrahim, 2020. "The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    Full references (including those not matched with items on IDEAS)

    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. Tatiane Fontana Ribeiro & Fernando A Peña-Ramírez & Renata Rojas Guerra & Gauss M Cordeiro, 2022. "Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-25, November.
    2. Mashail M. AL Sobhi, 2020. "The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    3. Helton Saulo & Roberto Vila & Giovanna V. Borges & Marcelo Bourguignon & Víctor Leiva & Carolina Marchant, 2023. "Modeling Income Data via New Parametric Quantile Regressions: Formulation, Computational Statistics, and Application," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    4. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    5. Shahid Mohammad & Kahadawala Cooray, 2025. "Lambda Exponential Family of Distributions With Properties and Applications," Journal of Probability and Statistics, John Wiley & Sons, vol. 2025(1).
    6. Guillermo Martínez-Flórez & Rafael B. Azevedo-Farias & Roger Tovar-Falón, 2022. "New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    7. Zubir Shah & Amjad Ali & Muhammad Hamraz & Dost Muhammad Khan & Zardad Khan & M. EL-Morshedy & Afrah Al-Bossly & Zahra Almaspoor, 2022. "A New Member of T‐X Family with Applications in Different Sectors," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jjmath:v:2022:y:2022:i:1:n:4288286. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

    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.