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A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data

Author

Listed:
  • Neveka M. Olmos

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

  • Emilio Gómez-Déniz

    (Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Osvaldo Venegas

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

  • Héctor W. Gómez

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

Abstract

The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution.

Suggested Citation

  • Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1631-:d:1400005
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    References listed on IDEAS

    as
    1. David Scollnik, 2007. "On composite lognormal-Pareto models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2007(1), pages 20-33.
    2. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    3. Teodorescu, Sandra & Vernic, Raluca, 2009. "Some Composite ExponentialPareto Models for Actuarial Prediction," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 82-100, December.
    4. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
    5. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    6. Calderín-Ojeda, Enrique & Azpitarte, Francisco & Gómez-Déniz, Emilio, 2016. "Modelling income data using two extensions of the exponential distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 756-766.
    7. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    9. Kahadawala Cooray & Chin-I Cheng, 2015. "Bayesian estimators of the lognormal–Pareto composite distribution," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(6), pages 500-515, August.
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