Research Article
BibTex RIS Cite

Matrix variate Laplace distribution: Properties and parameter estimation

Year 2018, Volume: 11 Issue: 1, 32 - 41, 29.06.2018

Abstract

In this study, we
proposed matrix variate Laplace distribution as a scale mixture of matrix
variate normal distribution and exponential distribution. Also, we examine some
distributional properties and give maximum likelihood estimators of its
parameters based on the EM algorithm.

References

  • [1] P. S. Laplace, 1774,Mémoire sur la probabilité des causes par les événemens, Mémoires de Mathématique et de Physique, 6, 621-656. English translation by S. M. Stigler Memoir on the Probability of the Causes of Events in Statistical Science, 1(3), 364-378, 1986.
  • [2] G. Ulrich, C. Chen, 1987, A bivariate double exponential distribution and its generalization, ASA Proceedings on Statistical Computing, 127-129.
  • [3] D. N. Anderson, 1992, A multivariate linnik distribution, Statistics and Probability Letters, 14, 333-,336.
  • [4] T. Eltoft, 2006, On the multivariate Laplace distribution, IEEE Signal Processing Letters, 13(5), 300-303.
  • [5] D. F. Andrews, C. L. Mallows, 1974, Scale mixtures of normal distributions, Journal of the Royal Statistical Society: Series B (Methodological), 36(1), 99-102.
  • [6] S. Kotz, T. J. Kozubowski, K. Podgorski, 2001, The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering and Finance.
  • [7] E. G. Sánchez-Manzano, M. A. Gómez-Villegas, J. Marín-Diazaraque, 2002, A matrix variate generalization of the power exponential family of distributions, Communications in Statistics-Theory and Methods, 31(12), 2167-2182.
  • [8] M. P. B. Gallaugher, P. D. McNicholas, 2017, Three skewed matrix variate distributions, arXiv:1704.02531v4a.
  • [9] A. K. Gupta, D. K. Nagar, 1999, Matrix variate distributions, Chapman and Hall/CRC, Boca Raton.
  • [10] A. P. Dempster, N. M. Laird, D. B. Rubin, 1977, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B (Methodological), 39(1), 1-38.
  • [11] O. E. Barndorff-Nielsen, 1997, Normal inverse gaussian distributions and stochastic volatility modelling, Scandinavian Journal of Statistics, 24(1), 1-13.

Matris değişkenli Laplace dağılımı: Özellikleri ve parametre tahmini

Year 2018, Volume: 11 Issue: 1, 32 - 41, 29.06.2018

Abstract

Bu
çalışmada matris değişkenli normal dağılım ve üstel dağılımın ölçek karması
olarak matris değişkenli Laplace dağılımı önerilmiştir. Ayrıca önerilen
dağılımın özellikleri incelenmiştir ve parametrelerinin tahmini için EM
(Expectation-Maximization) algoritmasına dayalı en çok olabilirlik tahmin edicileri
verilmiştir. 

References

  • [1] P. S. Laplace, 1774,Mémoire sur la probabilité des causes par les événemens, Mémoires de Mathématique et de Physique, 6, 621-656. English translation by S. M. Stigler Memoir on the Probability of the Causes of Events in Statistical Science, 1(3), 364-378, 1986.
  • [2] G. Ulrich, C. Chen, 1987, A bivariate double exponential distribution and its generalization, ASA Proceedings on Statistical Computing, 127-129.
  • [3] D. N. Anderson, 1992, A multivariate linnik distribution, Statistics and Probability Letters, 14, 333-,336.
  • [4] T. Eltoft, 2006, On the multivariate Laplace distribution, IEEE Signal Processing Letters, 13(5), 300-303.
  • [5] D. F. Andrews, C. L. Mallows, 1974, Scale mixtures of normal distributions, Journal of the Royal Statistical Society: Series B (Methodological), 36(1), 99-102.
  • [6] S. Kotz, T. J. Kozubowski, K. Podgorski, 2001, The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering and Finance.
  • [7] E. G. Sánchez-Manzano, M. A. Gómez-Villegas, J. Marín-Diazaraque, 2002, A matrix variate generalization of the power exponential family of distributions, Communications in Statistics-Theory and Methods, 31(12), 2167-2182.
  • [8] M. P. B. Gallaugher, P. D. McNicholas, 2017, Three skewed matrix variate distributions, arXiv:1704.02531v4a.
  • [9] A. K. Gupta, D. K. Nagar, 1999, Matrix variate distributions, Chapman and Hall/CRC, Boca Raton.
  • [10] A. P. Dempster, N. M. Laird, D. B. Rubin, 1977, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B (Methodological), 39(1), 1-38.
  • [11] O. E. Barndorff-Nielsen, 1997, Normal inverse gaussian distributions and stochastic volatility modelling, Scandinavian Journal of Statistics, 24(1), 1-13.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Y. Murat Bulut 0000-0002-0545-7339

Publication Date June 29, 2018
Published in Issue Year 2018 Volume: 11 Issue: 1

Cite

IEEE Y. M. Bulut, “Matris değişkenli Laplace dağılımı: Özellikleri ve parametre tahmini”, JSSA, vol. 11, no. 1, pp. 32–41, 2018.