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Quantile Estimation Using the Log-Skew-Normal Linear Regression Model with Application to Children’s Weight Data

Author

Listed:
  • Raúl Alejandro Morán-Vásquez

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Anlly Daniela Giraldo-Melo

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Mauricio A. Mazo-Lopera

    (Escuela de Estadística, Universidad Nacional de Colombia, Carrera 65 No. 59A-110, Medellín 050034, Colombia
    These authors contributed equally to this work.)

Abstract

In this article, we establish properties that relate quantiles of the log-skew-normal distribution to its parameters, allowing us to investigate the relationship between quantiles of a positive skewed response variable and a set of explanatory variables via the log-skew-normal linear regression model. We compute the maximum likelihood estimates of the parameters through a correspondence between the log-skew-normal and skew-normal linear regression models. Monte Carlo simulations show the satisfactory performance of the quantile estimators. An application to children’s data is presented and discussed.

Suggested Citation

  • Raúl Alejandro Morán-Vásquez & Anlly Daniela Giraldo-Melo & Mauricio A. Mazo-Lopera, 2023. "Quantile Estimation Using the Log-Skew-Normal Linear Regression Model with Application to Children’s Weight Data," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3736-:d:1229391
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    References listed on IDEAS

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    1. Adelchi Azzalini & Thomas Del Cappello & Samuel Kotz, 2002. "Log-Skew-Normal and Log-Skew-t Distributions as Models for Family Income Data," Journal of Income Distribution, Ad libros publications inc., vol. 11(3-4), pages 2-2, September.
    2. Jimmy Reyes & Yuri A. Iriarte, 2023. "A New Family of Modified Slash Distributions with Applications," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    3. Luis Vanegas & Gilberto Paula, 2015. "A semiparametric approach for joint modeling of median and skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 110-135, March.
    4. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    5. Liseo, Brunero & Loperfido, Nicola, 2003. "A Bayesian interpretation of the multivariate skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 395-401, February.
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