The Alpha-Beta-Gamma Skew Normal Distribution and Its Application
- 1 College of Science, Chongqing University of Technology, Chongqing, China
- 2 College of Science, Chongqing University of Technology, Chongqing, China
- 3 College of Science, Chongqing University of Technology, Chongqing, China
Abstract
In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.
- Azzalini, A. (1985) A Class of Distributions Which Includes the Normal Ones. Scandinavian Journal of Statistics, 12, 171-178.
- Arnold, B. and Beaver, R., Azzalini, A., Balakrishnan, N., Bhaumik, A., Dey, D., Cuadras, C., Sarabia, J., Arnold, B. and Beaver, R. (2002) Skewed Multivariate Models Related to Hidden Truncation and/or Selective Reporting. Test, 11, 7-54. https://doi.org/10.1007/BF02595728
- Gupta, R.C. and Gupta, R.D. (2004) Generalized Skew Normal Model. Test, 13, 501-524. https://doi.org/10.1007/BF02595784
- Yadegari, I., Gerami, A. and Khaledi, M.J. (2008) A Generalization of the Balakrishnan Skew-Normal Distribution. Statistics & Probability Letters, 78, 1165-1167. https://doi.org/10.1016/j.spl.2007.12.001
- Govind, A., Mudholkar, S., Alan, B. and Hutson, D. (2000) The Epsilon- Skew- Normal Distribution for Analyzing Near-Normal Data. Journal of Statistical Planning and Inference, 83, 291-309. https://doi.org/10.1016/S0378-3758(99)00096-8
- Behboodian, J., Jamalizadeh, A. and Balakrishnan, N. (2008) A New Class of Skew-Cauchy Distributions. Stats & Probability Letters, 76, 1488-1493, 2006. https://doi.org/10.1016/j.spl.2006.03.008
- Gupta, R.D. and Gupta, R.C. (2008) Analyzing Skewed Data by Power Normal Model. Test, 17, 197-210. https://doi.org/10.1007/s11749-006-0030-x
- Elal-Olivero, D. (2010) Alpha-Skew-Normal Distribution. Proyecciones (Antofagasta), 29, 224-240. https://doi.org/10.4067/S0716-09172010000300006
- Harandi, S.S. and Alamatsaz, M.H. (2013) Alpha-Skew-Laplace Distribution. Statistics & Probability Letters, 83, 774-782. https://doi.org/10.1016/j.spl.2012.11.024
- Sharafi, M., Sajjadnia, Z. and Behboodian, J. (2017) A New Generalization of Alpha-Skew-Normal Distribution. Communications in Statistics—Theory and Methods, 46, 6098-6111. https://doi.org/10.1080/03610926.2015.1117639
- Chakraborty, S., Jyoti Hazarika, P. and Shah, S. (2020) The Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. Malaysian Journal of Science, 39, 71-91. https://doi.org/10.22452/mjs.vol39no2.5
- Doostparast, M., Shafiei, S. and Jamalizadeh, A. (2016) The Alpha-Beta Skew Normal Distribution: Properties and Applications. Statistics, 50, 338-349.
- Roeder, K. (1990) Density Estimation with Confidence Sets Exemplified by Super Clusters and Voids in the Galaxies. Publications of the American Statal Association, 85, 617-624. https://doi.org/10.1080/01621459.1990.10474918