Two weighted models for skewed data

Document Type : Research Paper

Authors

Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

The skewed and weighted distributions may be considered as nice alternatives to fit a real data set in practical situations in which the well-known distributions are not suitable. The weighted distributions are first discussed and then two extensions of weighted models are proposed in this paper to analyze the skew data. The flexibility of the models is studied in view of the moment skewness coefficient for some cases. Finally, two real data sets are used to illustrate the results of the paper.

Keywords

Main Subjects

References

[1] Aleem, M., Sufyan, M., & Khan, NS. (2013). A Class of Modi ed Weighted Weibull Distribution and Its Properties.  American Review of Mathematics and Statistics, 1(1), 29-37. https://api.semanticscholar.org/CorpusID:125623946
[2] Arellano-Valle, RB., Gomez, HW., & Quintana, FA. (2004). A new class of skew-normal distribution. Communication in Statistics{Theory and Methods, 33, 1465-1480. https://doi.org/10.1081/STA-120037254
[3] Asgharzadeh, A., Esmaeili, L., & Shih, SH. (2013). A generalized skew logistic distribution. REVSTAT-Statistical Journal, 11(3), 317-338. https://doi.org/10.57805/revstat.v11i3.140
[4] Asgharzadeh, A., Esmaeili, L., & Nadarajah, S. (2016). Balakrishnan skew logistic distribution. Communications in Statistics-Theory and Methods, 42(2), 444-464. https://doi.org/10.1080/03610926.2013.823205
[5] Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171-178.
[6] Bahrami, W., Agahi, H., & Rangin, H. (2009). A two-parameter Balakrishnan skew-normal distribution. Journal of Statistical Research of Iran, 6(2), 231-242. https://doi.org/10.18869/acadpub.jsri.6.2.231
[7] Basalamah, D., Ning, W., & Gupta, A. (2018). The beta skew t distribution and its properties. Journal of Statistical Theory and Practice, 12(4), 837-860. https://doi.org/10.1080/15598608.2018.1481468
[8] Beranger, B., Padoan, SA., & Sisson, SA. (2019). Extremal properties of the univariate extended skew-normal distribution. Statistics & Probability Letters, 147, 73-82. https://doi.org/10.1016/j.spl.2018.09.018
[9] Das, J., Pathak, D., Hazarika, PJ., Chakraborty, S., & Hamedani, GG. (2023). A new exible alpha skew normal distribution. Journal of the Indian Society for Probability and Statistics, 24, 485-507. https://doi.org/10.1007/s41096-023-00163-8
[10] Fathi-Vajargah, B., & Hasanalipour, P. (2013). Introducing a novel bivariate generalized skew-symmetric normal distribution. Journal of Mathematics and Computer Science, 61, 266-271. https://doi.org/10.22436/jmcs.07.04.05
[11] Fisher, AA. (1934). The e ect of methods of ascertainment upon the estimation of frequencies. Annals of eugenics, 6(1), 13-25. https://doi.org/10.1111/j.1469-1809.1934.tb02105.x
[12] Gomez, HW., Venegas, O., & Bolfarin, H. (2007). Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics: The ocial journal of the International Environmetrics Society, 18(4), 395-407.
https://doi.org/10.1002/env.817
[13] Gupta, A., & Nadarajah, S. (2005). On the moments of the beta normal distribution. Communications in Statistics-Theory and Methods, 31(1), 1-13. https://doi.org/10.1081/STA-120026573
[14] Gui, W., & Guo, L. (2018). Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution. Indian Journal of Pure and Applied Mathematics, 49, 633-650. https://doi.org/10.1007/s13226-018-0291-6
[15] Hasanalipour, P., & Razmkhah, M. (2021). Inference on skew-normal distribution based on Fisher information in order statistics. Communications in Statistics-Simulation and Computation, 51(4), 1525-1541. https://doi.org/10.1080/03610918.2019.1674869
[16] Hasanalipour, P., & Razmkhah, M. (2022). Testing skew-symmetry based on extreme ranked set sampling. Statistical Papers, 62, 2311-2332. https://doi.org/10.1007/s00362-020-01183-3
[17] Hasanalipour, P., Hassani Oskouei, L., Jabbari Khamnei, H., & Khorshidian, K. (2017). The beta skew-generalized normal distribution. Communications in Statistics-Theory and Methods, 46, 2270-2276. https://doi.org/10.1080/03610926.2015.1041980
[18] Hasanalipour, P., & Shara , M. (2012). A new generalized Balakrishnan skew-normal distribution. Statistical Papers, 53, 219-228. https://doi.org/10.1007/s00362-010-0330-9 
[19] Hazarika, PJ.,Shah, S., Chakraborty, S., Alizadeh, M., & Hamedani, G. (2023). Multimodal alpha skew normal distribution: A new distribution to model skewed multi-modal observations. Pakistan Journal of Statistics and Operation Research, 19, 747-763. https://doi.org/10.18187/pjsor.v19i4.4232
[20] Jamalizadeh, A., Behboodian, J., & Balakrishnan, N. (2008). A two-parameter generalized skew-normal distribution. Statistics & Probability Letters, 78(13), 1722-1726. https://doi.org/10.1016/j.spl.2008.01.006
[21] Jones, M. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43. https://doi.org/10.1007/BF02602999
[22] Kazemi, MR., Haghbin, H., & Behboodian, J. (2011). Another generalization of the skew normal distribution. World Applied Sciences Journal, 12(7), 1034-1039. 
[23] Mameli, V. (2015). The Kumaraswamy skew-normal distribution. Statistics & Probability Letters, 104, 75-81. https://doi.org/10.1016/j.spl.2015.04.031
[24] Mameli, V., & Musio, M. (2013). A generalization of the skew-normal distribution: the beta skew-normal. Communications in Statistics-Theory and Methods, 42(12), 2229-2244. https://doi.org/10.1007/s10440-006-9017-6
[25] Mirzadeh, S., & Iranmanesh, A. (2019). A new class of skew-logistic distribution. Mathematical Sciences, 13, 375-385. https://doi.org/10.1007/s40096-019-00306-8 
[26] Nadarajah, S., & Kotz, S. (2006). Skew distributions generated from di erent families. Acta Applicanda Mathematica, 91(1), 1-37. https://doi.org/10.1007/s10440-006-9017-6
[27] Naghibi, F., Alavi, S.M.R ., & Chinipardaz, R. (2022). A New Weighted Skew Normal Model. STATISTICS, OPTIMIZATION AND INFORMATION COMPUTING, 10, 1126-1142. https://doi.org/10.19139/soic-2310-5070-1108
[28] Rao, CR. (1965). On discrete distributions arising out of methods of ascertainment. Sankhya: The Indian Journal of Statistics, Series A, 27(2), 311-324. 
[29] Rasekhi, M., Chinipardaz, R., & Alavi, SMR. (2016). A  exible generalization of the skew normal distribution based on a weighted normal distribution. Statistical Methods & Applications, 25, 375-394. https://doi.org/10.1007/s10260-015-0337-4 
[30] Saghir, A., Hamedani, G., Tazeem, S., & Khadim, A. (2018). Weighted Distributions: A Brief Review, Perspective and Characterizations. International Journal of Statistics and Probability, 7(1), 39-71. https://doi.org/10.5539/ijsp.v6n3p109 
[31] Shara , M., & Behboodian, J. (2008). The Balakrishnan skew-normal density. Statistical Papers, 49, 769-778. https://doi.org/10.1007/s00362-006-0038-z

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History

  • Receive Date: 25 October 2024
  • Revise Date: 10 April 2025
  • Accept Date: 20 May 2025

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