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Lambda Exponential Family of Distributions With Properties and Applications

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  • Shahid Mohammad
  • Kahadawala Cooray

Abstract

This research introduces a new family of probability distributions called the lambda exponential (LE) family. These distributions are constructed by multiplying an exponential density function with a continuous cumulative distribution function. A key motivation is obtaining closed‐form solutions for the moment‐generating function. Various mathematical properties of the LE family are investigated. As a specific case, the inverse Gaussian (IG) cumulative distribution function is used to derive the lambda exponential inverse Gaussian (LE‐IG) distribution and study its characteristics. Performance of maximum likelihood estimation is assessed through simulations using the quantile function. To demonstrate flexibility and applicability, the LE family is fitted to two real datasets and compared to other distributions via likelihood methods.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:8847851
    DOI: 10.1155/jpas/8847851
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    References listed on IDEAS

    as
    1. Ahmed Z. Afify & Osama Abdo Mohamed, 2020. "A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    2. Shahid Mohammad & Isabel Mendoza, 2025. "A New Hyperbolic Tangent Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 12(2), pages 457-480, April.
    3. Egemen Ozkan & Gulhayat Golbasi Simsek, 2023. "Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications," PLOS ONE, Public Library of Science, vol. 18(1), pages 1-22, January.
    4. 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.
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