[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: ::
Back to the articles list Back to browse issues page
Development of a Bayesian Model For Finite Mixture Regression of the Skew-Laplace Distribution
Bahram Tarami , Nahid Sanjari Farsipour * , Hassan Khosravi
Abstract:   (25 Views)
In many applications, observations have a skewness, an elongated shape, a heavy tail, a multi-mode structure, or a mixed distribution. Therefore, models based on the normal distribution cannot provide correct inferences under such conditions and can lead to biased estimators or increased variance. The Laplace distribution and its generalizations can be suitable alternatives in such situations due to their elongation, heavy tails, and skewness. On the other hand, in models based on mixed distributions, there is always a possibility that fewer samples are available from one or more components. Therefore, given the Bayesian approach's advantage in handling small samples, this research developed a Bayesian model to fit a finite mixed regression model with skew-Laplace distributions and conducted a simulation study to assess its performance. Laplace has been compared in two approaches, frequentist and Bayesian. The results show that the Bayesian approach of the model is more effective than other  models.
Keywords: Skew-Laplace distribution, Mixture regresion, Metropolis-Hastings algorithm.
Full-Text [PDF 6568 kb]   (26 Downloads)    
Type of Study: Research | Subject: Statistical Inference
Received: 2024/06/21 | Accepted: 2025/04/30
References
1. امیری دوباری، پ.، نادری، م، جمالیزاده، ا. (1397)، توزیع چوله-لاپلاس موزون دو پارامتری، مجله علوم آماری، 12(2)، 351-364.
2. Aitkin, M. and Wilson, G. T. (1980), Mixture Models, Outliers and EM Algorithm, Technometrics, 22, 325-331. [DOI:10.1080/00401706.1980.10486163]
3. Akaike, H. (1973), Information theory and an extension of the maximum likelihood principle.
4. Amiri Domari P, Naderi M, Jamalizadeh A. The Two-parameter Weighted Skew Laplace Distribution. Journal of Statistical Sciences, 12(2), 351-364 [DOI:10.29252/jss.12.2.351]
5. Arslan, O. (2009), An Alternative Multivariate Skew Laplace Distribution: Properties and Estimation, Statistical Papers, 49(1), 1-23.
6. Bai, Z.D., Krishnaiah, P.R. and Zhao, L.C. (2005), On Rates of Convergence of Efficient Detection Criteria in Signal Processing with White Noise, IEEE Trans Inform Theor, 35, 380-388. [DOI:10.1109/18.32132]
7. Bohning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. (1994), The Distribution of the Likelihood Ratio for Mixtures of Densities from the One Parameter Exponential Family, Annals of the Institute of Statistical Mathematics, 46, 373-388. [DOI:10.1007/BF01720593]
8. Cancho, V. G., Dey, K. D., Lachos, V. H. and Andrade, M. (2010), Bayesian Nonlinear Regression Models with Scale Mixtures of Skew Normal Distributions: Estimation and Case Influence Diagnostics, Computational Statistics and Data Analysis, 55, 588-602. [DOI:10.1016/j.csda.2010.05.032]
9. Dogru, F.Z. and Arslan, O. (2017), Robust Mixture Regression based on the Skew t Distribution, [DOI:10.15446/rce.v40n1.53580]
10. Revista Colombiana de Estadística, 40(1), 45-64.
11. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977), Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of Royal Statistical Society, 39, 1-38. [DOI:10.1111/j.2517-6161.1977.tb01600.x]
12. DeSarbo, W. S. and Corn, W. L. (1988), A Maximum Likelihood Methodology for Clusterwise linear regression, Journal of Classification, 5, 249-282. [DOI:10.1007/BF01897167]
13. Diebolt, J. and Robert, C.P. (1990), Bayesian Estimation of Finite Mixture Distributions: Part II, Sampling Implementation, Technical Report III. Paris: Laboratoire de Statistique Thorique et Applique, Universit Paris VI.
14. Gelman, A., Jakulin, A., Grazia Pittau, M. and Su, Y. (2008), A Weakly Informative Default Prior Distribution for Logistic and other Regression Models, The Annals of Applied Statistics, 4, 1360-1383. [DOI:10.1214/08-AOAS191]
15. Hawkins, D. S., Allen, D. M. and Stomber, A. J. (2001), Determining the Number of Components in Mixtures of Linear Models, Computational Statistics & Data Analysis, 38, 15-48. [DOI:10.1016/S0167-9473(01)00017-2]
16. Holla, M.S. and Bhattacharya, S.K. (1986), On a Compound Gaussian Distribution, Annals of the Institute of Statistical Mathematics, 20, 331-336. [DOI:10.1007/BF02911647]
17. Jones, P. N. and McLachlan, G. J. (1992), Fitting Finite Mixture Models in a Regression Context, [DOI:10.1111/j.1467-842X.1992.tb01356.x]
18. Austrian Journal of Statistics, 34, 233-240.
19. Julia, O. and Vives-Rego, J. (2005), Skew-Laplace Distribution in Gramnegative Bacterial Axenic Cultures: New Insights into Intrinsic Cellular Heterogeneity, Microbiology, 151, 749-755. [DOI:10.1099/mic.0.27460-0] [PMID]
20. Kotz, S., Kozubowski, T.J. and Podgorski, K. (2001), The Laplace Distribution and Generalizations, Birkhauser, Boston. [DOI:10.1007/978-1-4612-0173-1]
21. Lachos, V., Ghosh, P. and Arellano-Valle, R. (2010), Likelihood Based Inference for Skew Normal/Independent Linear Mixed Model, Statistica Sinica, 20, 303-322.
22. Laplace, P.S. (1774), Memoire sur la probability des causes par les evenements, Memoires de mathematic et de physique, 6, 621-656.
23. Lavine, M. and West, M. (1992), A Bayesian Method of Classification and Discrimination, Canadian Journal of Statistics, 20, 451-461. [DOI:10.2307/3315614]
24. Lindsay, B. G. (1995), Mixture Models: Theory Geometry and Applications, Hayward, California: Institute of Mathematical Statistics. [DOI:10.1214/cbms/1462106013]
25. Maclachlan, G. and Peel, D. (2000), Finite Mixture Models, Wiley, New York. [DOI:10.1002/0471721182]
26. Marin, J. M., Mengersen, K. and Robert, C. (2005), Bayesian Modelling and Inference on Mixtures of Distributions, Handbook of Statistics, 25, Springer-Verlag, New York. [DOI:10.1016/S0169-7161(05)25016-2]
27. Pearson, K. (1894), Contributions to the Theory of Mathematical Evolution, Philosiphical Transitions of the Royal Society of London, 185, 71-110. [DOI:10.1098/rsta.1894.0003]
28. Purdom, E. and Holmes, S.P. (2005), Error Distribution for Gene Expression data, [DOI:10.2202/1544-6115.1070] [PMID]
29. Statistical Applications in Genetics and Molecular Biology, 4(1), 1-35.
30. Quandt, R.E. (1972), A New Approach to Estimating Switching Regressions, Journal of the American Statistical Association, 67, 306-310. [DOI:10.1080/01621459.1972.10482378]
31. Quandt, R. E. and Ramsey, J. B. (1978), Estimating Mixtures of Normal Distributions and Switching Regressions, Journal of the American Statistical Association, 73, 730-738. [DOI:10.1080/01621459.1978.10480085]
32. Richardson, S. and Green, P.G. (1997), On Bayesian analysis of mixtures with an unknown number of components (with discussion), Journal of the Royal Statistical Society, 59, 731-792. [DOI:10.1111/1467-9868.00095]
33. Roeder, K. and Wasserman, L. (1997), Practical Bayesian Density Estimation using mixture of Normal, [DOI:10.2307/2965553]
34. Journal of the American Statistical Association, 92, 894-902. [DOI:10.1001/jama.1929.02700370050018]
35. Song, W., Yao, W. and Xing, Y. (2014), Robust Mixture Regression Model Fitting by Laplace Distribution, [DOI:10.1016/j.csda.2013.06.022]
36. Computational Statistics and Data Analysis, 71, 128-137.
37. Tarami, B., Sanjari Farsipour, N. and Khosravi, H. (2024), Bayesian Mixture Regression Approach based on Laplace Distribution, Journal of Mathematical Research.
38. Turner, T. R. (2000), Estimating the Propagation Rate of a Viral Infection of Potato Plants Via Mixtures of Regressions, Journal of Applied Statistics, 49(3), 371-384. [DOI:10.1111/1467-9876.00198]
39. Wolfe, J. H. (1965), A Computer Program for the Computation of Maximum Likelihood Analysis of Types, Research Memo. SRM 65-12. San Diego: U.S. Naval Personal Research Activity. [DOI:10.21236/AD0620026]
40. Yao, W., Wei, Y. and Yu, C. (2014), Robust Mixture Regression using the distribution, Computational Statistics and Data Analysis, 71, 116-127. [DOI:10.1016/j.csda.2013.07.019]
41. Yu, K. and Zhang, J. (2005), A Three-Parameter Asymmetric Laplace Distribution and its Extension, Communications in Statistics-Theory and Methods, 34, 1867- 1879. [DOI:10.1080/03610920500199018]
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA


XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Back to the articles list Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.2 seconds with 45 queries by YEKTAWEB 4722