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A Bivariate Power Lindley Survival Distribution

Author

Listed:
  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba 2300, Colombia)

  • Barry C. Arnold

    (Statistics Department, University of California Riverside, Riverside, CA 92521, USA)

  • Héctor W. Gómez

    (Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

We introduce and investigate the properties of new families of univariate and bivariate distributions based on the survival function of the Lindley distribution. The univariate distribution, to reflect the nature of its construction, is called a power Lindley survival distribution. The basic distributional properties of this model are described. Maximum likelihood estimates of the parameters of the distribution are studied and the corresponding information matrix is identified. A bivariate power Lindley survival distribution is introduced using the technique of conditional specification. The corresponding joint density and marginal and conditional densities are derived. The product moments of the distribution are obtained, together with bounds on the range of correlations that can be exhibited by the model. Estimation of the parameters of the model is implemented by maximizing the corresponding pseudo-likelihood function. The asymptotic variance–covariance matrix of these estimates is investigated. A simulation study is performed to illustrate the performance of these parameter estimates. Finally some examples of model fitting using real-world data sets are described.

Suggested Citation

  • Guillermo Martínez-Flórez & Barry C. Arnold & Héctor W. Gómez, 2024. "A Bivariate Power Lindley Survival Distribution," Mathematics, MDPI, vol. 12(21), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3334-:d:1505749
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    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. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    3. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    4. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
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