A new class of weighted bimodal distribution with application to gamma-ray burst duration data

References

• S. Acitas, B. Senoglu, and O. Arslan, Alpha–Skew generalized t distribution, Rev. Colomb. Estadíst. 38 (2015), pp. 353–370. doi: 10.15446/rce.v38n2.51666
   Google Scholar
• S.M.R. Alavi and R. Chinipardaz, A useful distribution for symmetric and bimodal data, Statistics 1 (2014), pp. 25–41.
   Google Scholar
• R.B. Arellano-Valle, H.W. Gómez, and F.A. Quintana, A new class of skew-normal distributions, Comm. Statist. Theory Methods 33 (2004), pp. 1465–1480. doi: 10.1081/STA-120037254
   Web of Science ®Google Scholar
• R.B. Arellano-Valle, H.W. Gómez, and F.A. Quintana, Statistical inference for a general class of asymmetric distributions, J. Statist. Plann. Inference 128 (2005), pp. 427–443. doi: 10.1016/j.jspi.2003.11.014
   Web of Science ®Google Scholar
• B.C. Arnold, H.W. Gómez, and H.S. Salinas, On multiple constraint skewed models, Statistics 43 (2009), pp. 279-–293. doi: 10.1080/02331880802357914
   Web of Science ®Google Scholar
• J. Arrué, H.W. Gómez, H.S. Salinas, and H. Bolfarine, A new class of Skew-Normal-Cauchy distribution, Sort-Stat Oper Res T 39 (2015), pp. 35-–50.
   Web of Science ®Google Scholar
• A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Stat. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• J. Behboodian, M. Sharafi, Z. Sajjadnia, and M. Zarepour, The bimodal standard normal density and kurtosis, AUT J. Math. Comput. 1 (2020), pp. 17–25.
   Google Scholar
• J.E. Contreras-Reyes, M. Maleki, and D.D. Cortés, Skew-Reflected-Gompertz information quantilers with application to sea surface temperature records, Mathematics 7 (2019), p. 403. doi: 10.3390/math7050403
   Web of Science ®Google Scholar
• D. Dierickx, B. Basu, J. Vleugels, and O. Van der Biest, Statistical extreme value modeling of particle size distributions: experimental grain size distribution type estimation and parameterization of sintered zirconia, Mater. Characteriz. 45 (2000), pp. 61–70. doi: 10.1016/S1044-5803(00)00049-8
   Web of Science ®Google Scholar
• D. Elal-Olivero, Alpha-skew-normal distribution, Proyecciones 29 (2010), pp. 224–240.
   Google Scholar
• D. Elal-Olivero, H.W. Gómez, and F.A. Quintana, Bayesian modeling using a class of bimodal skew-elliptical distributions, J. Statist. Plann. Inference 139 (2009), pp. 1484–1492. doi: 10.1016/j.jspi.2008.07.016
   Web of Science ®Google Scholar
• A. Ertel, Bimodal gene expression and biomarker discovery, Cancer Inform. 9 (2010), pp. 11–14. doi: 10.4137/CIN.S3456
   PubMedGoogle Scholar
• M.G. Genton and N. Loperfido, Generalized skew-elliptical distributions and their quadratic forms, Ann. Inst. Statist. Math. 57 (2005), pp. 389–401. doi: 10.1007/BF02507031
   Web of Science ®Google Scholar
• P.J. Hazarika and S. Chakraborty, Alpha skew logistic distribution, IOSR J. Math. 10 (2014), pp. 36–46. doi: 10.9790/5728-10463646
   Google Scholar
• P.J. Hazarika and S. Chakraborty, A note on alpha skew generalized logistic distribution, IOSR J. Math. 11 (2015), pp. 85–88.
   Google Scholar
• A. Hoseinzadeh, M. Maleki, Z. Khodadadi, and J.E. Contreras-Reyes, The Skew-Reflected-Gompertz distribution for analyzing symmetric and asymmetric data, J. Comput. Appl. Math. 349 (2019), pp. 132–141. doi: 10.1016/j.cam.2018.09.011
   Web of Science ®Google Scholar
• W.J. Huang, N.C. Su, and H.Y. Teng, On some study of skew-t distribution, Comm. Statist. Theory Methods 48 (2019), pp. 4712–4729. doi: 10.1080/03610926.2012.700369
   Web of Science ®Google Scholar
• M.C. Jones and A. Pewsey, Sinh–arcsinh distributions, Biometrika 96 (2009), pp. 761–780. doi: 10.1093/biomet/asp053
   Web of Science ®Google Scholar
• H.J. Kim, On a class of two-piece skew-normal distributions, Statistics 39 (2005), pp. 537-–553. doi: 10.1080/02331880500366027
   Web of Science ®Google Scholar
• C. Kouveliotou, C.A. Meegan, G.J. Fishman, N.P. Bhat, M.S. Briggs, T.M. Koshut, W.S. Paciesas, and G.N. Pendleton, Identification of two classes of gamma-ray bursts, Astrophys. J. 413 (1993), pp. 101–104. doi: 10.1086/186969
   Web of Science ®Google Scholar
• H.S. Kwong and S. Nadarajah, A note on analysis of gamma-ray burst duration distribution using mixtures of skewed distributions, Monthly Not. R. Astronom. Soc. 473 (2018), pp. 625-–646. doi: 10.1093/mnras/stx2373
   Web of Science ®Google Scholar
• T.I. Lin, J.C. Lee, and S.Y. Yen, Finite mixture modeling using the skew-normal distribution, Statist. Sinica 17 (2007), pp. 909–927.
   Web of Science ®Google Scholar
• E.P. Mazets, S.V. Golenetskii, V.N. Il'Inskii, V.N. Panov, R.L. Aptekar, Y.A. Gur'Yan, M.P. Proskura, I.A. Sokolov, Z.Y. Sokolova, T.V. Kharitonova, and A.V. Dyatchkov, Catalog of cosmic gamma-ray bursts from the KONUS experiment data-parts I and II, Astrophys. Space Sci. 80 (1981), pp. 3-–83. doi: 10.1007/BF00649140
   Google Scholar
• G.J. McLachlan and D. Peel, Finite Mixture Models, Wiley, New York, 2000.
   Google Scholar
• G.S. Mudholkar and A.D. Hutson, The epsilon-skew-normal distribution for analyzing near normal data, J. Statist. Plann. Inference. 83 (2000), pp. 291–309. doi: 10.1016/S0378-3758(99)00096-8
   Web of Science ®Google Scholar
• S. Nadarajah and S. Kotz, Skew distributions generated from different families, Acta Appl. Math. 91 (2004), pp. 1–37. doi: 10.1007/s10440-006-9017-6
   Web of Science ®Google Scholar
• E. Nakar, Short-hard gamma-ray bursts, Phys. Rep. 442 (2007), pp. 166–236. doi: 10.1016/j.physrep.2007.02.005
   Google Scholar
• G.P. Patil, Weighted Distributions, In Encyclopedia of Environmetrics, John Wiley, 2002, pp. 2369–2377.
   Google Scholar
• G.P. Patil and C.R. Rao, The weighted distributions: a survey of their applications, In Applications of Statistics, North-Holland, 1977, pp. 383–405.
   Google Scholar
• K. Pearson, Das Fehlergesetz und seine Verallgemeinerungen Durch Fechner und Pearson. A Rejoinder. Biometrika, 4 (1905), pp. 169–212.
   Google Scholar
• J. Sanchez and Y. He, Internet data analysis for the undergraduate statistics curriculum, J. Statist. Educ. 13 (2005), pp. 1–20. doi: 10.1080/10691898.2005.11910568
   Google Scholar
• S. Shams Harandi and M. Alamatsaz, Alpha-skew-laplace distribution, Statist. Probab. Lett. 83 (2013), pp. 774–782. doi: 10.1016/j.spl.2012.11.024
   Web of Science ®Google Scholar
• S. Shams Harandi and M.H. Alamatsaz, Discrete alpha-skew-Laplace distribution, SORT 39 (2015), pp. 71–84.
   Web of Science ®Google Scholar
• M. Sharafi, Z. Sajjadnia, and J. Behboodian, A new generalization of alpha-skew-normal distribution, Comm. Statist. Theory Methods 46 (2017), pp. 6098–6111. doi: 10.1080/03610926.2015.1117639
   Web of Science ®Google Scholar
• M. Tarnopolski, Analysis of the observed and intrinsic durations of gamma-ray bursts with known redshift, Astrophys. Space Sci. 361 (2016). doi: 10.1007/s10509-016-2687-2
   Web of Science ®Google Scholar
• M. Tarnopolski, Analysis of gamma-ray burst duration distribution using mixtures of skewed distributions, Monthly Not. R. Astronom. Soc. 458 (2016), pp. 2024–2031. doi: 10.1093/mnras/stw429
   Web of Science ®Google Scholar
• R.S. Tsay, Analysis of Financial Time Series, 3rd ed., John Wiley, New York, 2010.
   Google Scholar
• J. Wang, S. Wen, W.F. Symmans, L. Pusztai, and K.R. Coombes, The bimodality index: a criterion for discovering and ranking bimodal signatures from cancer gene expression profiling data, Cancer Inform. 7 (2009), pp. 199–216.
   PubMedGoogle Scholar
• S.E. Woosley and J.S. Bloom, The supernova-gamma-ray burst connection, Ann. Rev. Astronom. Astrophys. 44 (2006), pp. 507–556. doi: 10.1146/annurev.astro.43.072103.150558
   Web of Science ®Google Scholar
• C. Zhang, B.E. Mapes, and B.J. Soden, Bimodality in tropical water vapor, Quart. J. Roy. Meteorol 129 (2003), pp. 2847–2866. doi: 10.1256/qj.02.166
   Web of Science ®Google Scholar