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Maximum likelihood parameter estimation for the multivariate skew-slash distribution

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  • Arslan, Olcay

Abstract

In this paper we consider the parameter estimation of the multivariate skew-slash distribution introduced by Arslan [Arslan, O. 2008. An alternative multivariate skew-slash distribution. Statistics and Probability Letters 78, 2756-2761], which is a recent example of the normal variance-mean mixture distributions. Due to the complexity of the likelihood function, estimation of its parameters by direct maximization of the likelihood function seems difficult. To overcome this problem, we propose a simple EM-based maximum likelihood estimation procedure to estimate the parameters of the multivariate skew-slash distribution. We provide three examples to demonstrate the modeling strength of the multivariate skew-slash distribution and the feasibility of the proposed EM algorithm.

Suggested Citation

  • Arslan, Olcay, 2009. "Maximum likelihood parameter estimation for the multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2158-2165, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:20:p:2158-2165
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    References listed on IDEAS

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    1. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    2. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    3. DiCiccio T.J. & Monti A.C., 2004. "Inferential Aspects of the Skew Exponential Power Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 439-450, January.
    4. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
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    Cited by:

    1. Sukru Acitas & Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2013. "One-step M -estimators: Jones and Faddy's skewed t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1545-1560, July.
    2. del Castillo, J.M., 2016. "Slash distributions of the sum of independent logistic random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 111-118.
    3. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    4. 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.
    5. Hainan Guo & David Goldsman & Kwok-Leung Tsui & Yu Zhou & Shui-Yee Wong, 2016. "Using simulation and optimisation to characterise durations of emergency department service times with incomplete data," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6494-6511, November.
    6. Bulut, Y. Murat & Arslan, Olcay, 2015. "Matrix variate slash distribution," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 173-178.
    7. M. Arendarczyk & T. J. Kozubowski & A. K. Panorska, 2023. "Slash distributions, generalized convolutions, and extremes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 593-617, August.

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