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The Odd Log-Logistic Student t Distribution: Theory and Applications

Author

Listed:
  • Altemir Silva Braga

    (Universidade de São Paulo)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco)

  • Edwin M. M. Ortega

    (Universidade de São Paulo)

  • Giovana O. Silva

    (Universidade Federal da Bahia)

Abstract

The normal distribution is most used in analysis of experiments. However, it is not suitable to apply in situations where the data have evidence of bimodality or heavier tails than the normal distribution. So, we propose a new four-parameter model called the odd log-logistic Student t distribution as an alternative to the normal and Student t distributions. The new distribution can be symmetric, platykurtic, mesokurtic or leptokurtic and may be unimodal or bimodal. Its various structural properties can be determined from the linear representation of its density function. The estimation of the model parameters is performed by maximum likelihood. The proposed distribution can be used as an alternative for randomized complete block design, thus providing analysis of real data more realistic than other special regression models. We perform a sensitivity analysis to detect influential or outlying observations, and construct generated envelopes from the residuals to select appropriate models. We illustrate the importance of the proposed model by means of three real data sets in analysis of experiments carried out in different regions of Brazil.

Suggested Citation

  • Altemir Silva Braga & Gauss M. Cordeiro & Edwin M. M. Ortega & Giovana O. Silva, 2017. "The Odd Log-Logistic Student t Distribution: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 615-639, December.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0301-x
    DOI: 10.1007/s13253-017-0301-x
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    References listed on IDEAS

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    1. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    2. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    4. Nadarajah, Saralees & Gupta, Arjun K., 2007. "A generalized gamma distribution with application to drought data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 1-7.
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    Cited by:

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    2. Gauss Moutinho Cordeiro & Maria Do Carmo Soares De Lima & Edwin Moisés Marcos Ortega & Adriano Kamimura Suzuki, 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications," Stats, MDPI, vol. 1(1), pages 1-16, May.

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