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Published in: Annals of Data Science 4/2023

15-04-2021

A Generalized-Alpha–Beta-Skew Normal Distribution with Applications

Authors: Sricharan Shah, Partha Jyoti Hazarika, Subrata Chakraborty, M. Masoom Ali

Published in: Annals of Data Science | Issue 4/2023

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Abstract

Recently there is a lot of research related to skewed distributions and their growing relevance in data analytics. In the present work we introduce a new generalized version of alpha beta skew normal distribution and some of its basic properties are investigated. Some extensions of the proposed distribution have also been studied. A simulation study has been conducted to see the performance of the obtained estimators of the parameters using Metropolis–Hastings (MH) algorithm. The appropriateness of the proposed distribution has been tested by comparing it with twelve closely related and nested distributions using Akaike Information Criterion. The Likelihood Ratio test has been employed for testing the relevance of the induction of the additional parameters in the proposed model.

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Appendix
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Literature
1.
go back to reference Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining (Vol. 10, pp. 2250–2254). New York: McGraw-Hill/Irwin Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining (Vol. 10, pp. 2250–2254). New York: McGraw-Hill/Irwin
2.
go back to reference Shi Y, Tian Y, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer Shi Y, Tian Y, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer
3.
go back to reference Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178CrossRef Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178CrossRef
4.
go back to reference Cormode G, Muthukrishnan S (2005) Summarizing and mining skewed data streams. In: Proceedings of the 2005 SIAM international conference on data mining. Society for Industrial and Applied Mathematics, pp 44–55 Cormode G, Muthukrishnan S (2005) Summarizing and mining skewed data streams. In: Proceedings of the 2005 SIAM international conference on data mining. Society for Industrial and Applied Mathematics, pp 44–55
5.
go back to reference Manning W (2012) Dealing with skewed data on costs and expenditures. In: The Elgar companion to health economics, 2nd Edition. Edward Elgar Publishing Manning W (2012) Dealing with skewed data on costs and expenditures. In: The Elgar companion to health economics, 2nd Edition. Edward Elgar Publishing
6.
go back to reference Theodossiou P (1998) Financial data and the skewed generalized t distribution. Manag Sci 44(12-part-1):1650–1661CrossRef Theodossiou P (1998) Financial data and the skewed generalized t distribution. Manag Sci 44(12-part-1):1650–1661CrossRef
7.
go back to reference Juárez MA, Steel MF (2010) Model-based clustering of non-Gaussian panel data based on skew-t distributions. J Bus Econ Stat 28(1):52–66CrossRef Juárez MA, Steel MF (2010) Model-based clustering of non-Gaussian panel data based on skew-t distributions. J Bus Econ Stat 28(1):52–66CrossRef
8.
go back to reference Gao J, Fan W, Han J, Yu PS (2007) A general framework for mining concept-drifting data streams with skewed distributions. In: Proceedings of the 2007 SIAM international conference on data mining. Society for Industrial and Applied Mathematics, pp 3–14 Gao J, Fan W, Han J, Yu PS (2007) A general framework for mining concept-drifting data streams with skewed distributions. In: Proceedings of the 2007 SIAM international conference on data mining. Society for Industrial and Applied Mathematics, pp 3–14
9.
go back to reference Hammel I, Lagunoff D, Bauza M, Chi E (1983) Periodic, multimodal distribution of granule volumes in mast cells. Cell Tissue Res 228(1):51–59CrossRef Hammel I, Lagunoff D, Bauza M, Chi E (1983) Periodic, multimodal distribution of granule volumes in mast cells. Cell Tissue Res 228(1):51–59CrossRef
10.
go back to reference Dimitrov B, JrD G, Chukova S (1997) Probability distributions in periodic random environment and their applications. SIAM J Appl Math 57(2):501–517CrossRef Dimitrov B, JrD G, Chukova S (1997) Probability distributions in periodic random environment and their applications. SIAM J Appl Math 57(2):501–517CrossRef
11.
go back to reference Sinha RK (2012) A thought on exotic statistical distributions. World Acad Sci Eng Technol 61:366–369 Sinha RK (2012) A thought on exotic statistical distributions. World Acad Sci Eng Technol 61:366–369
12.
go back to reference Chakraborty S, Hazarika PJ (2011) A survey of the theoretical developments in univariate skew normal distributions. Assam Stat Rev 25(1):41–63 Chakraborty S, Hazarika PJ (2011) A survey of the theoretical developments in univariate skew normal distributions. Assam Stat Rev 25(1):41–63
13.
go back to reference Chakraborty S, Hazarika PJ, Ali MM (2015) A multimodal skewed extension of normal distribution: its properties and applications. Statistics 49(4):859–877CrossRef Chakraborty S, Hazarika PJ, Ali MM (2015) A multimodal skewed extension of normal distribution: its properties and applications. Statistics 49(4):859–877CrossRef
14.
go back to reference Shah S, Hazarika PJ, Chakraborty S, Ali MM (2020) The Log-Balakrishnan-alpha-skew-normal distribution and its applications. Pak J Stat Oper Res 16(1):109–117CrossRef Shah S, Hazarika PJ, Chakraborty S, Ali MM (2020) The Log-Balakrishnan-alpha-skew-normal distribution and its applications. Pak J Stat Oper Res 16(1):109–117CrossRef
15.
go back to reference Shah S, Hazarika PJ, Chakraborty S (2020) A new alpha skew laplace distribution: properties and its applications. Int J Agric Stat Sci 16(1):1–10 Shah S, Hazarika PJ, Chakraborty S (2020) A new alpha skew laplace distribution: properties and its applications. Int J Agric Stat Sci 16(1):1–10
16.
go back to reference Shah S, Chakraborty S, Hazarika PJ (2020) The Balakrishnan alpha skew logistic distribution: properties and applications. Int J Appl Math Stat 59(1):76–92 Shah S, Chakraborty S, Hazarika PJ (2020) The Balakrishnan alpha skew logistic distribution: properties and applications. Int J Appl Math Stat 59(1):76–92
17.
go back to reference Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Statist 12:171–178 Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Statist 12:171–178
18.
go back to reference Elal-Olivero D (2010) Alpha-skew-normal distribution. Proyecciones (Antofagasta) 29(3):224–240CrossRef Elal-Olivero D (2010) Alpha-skew-normal distribution. Proyecciones (Antofagasta) 29(3):224–240CrossRef
19.
go back to reference Shafiei S, Doostparast M, Jamalizadeh A (2016) The alpha–beta skew normal distribution: properties and applications. Statistics 50(2):338–349 Shafiei S, Doostparast M, Jamalizadeh A (2016) The alpha–beta skew normal distribution: properties and applications. Statistics 50(2):338–349
20.
go back to reference Venegas O, Bolfarine H, Gallardo DI, Vergara-Fernández A, Gómez HW (2016) A note on the log alpha skew normal model with geochemical applications. Appl Math 10(5):1697–1703 Venegas O, Bolfarine H, Gallardo DI, Vergara-Fernández A, Gómez HW (2016) A note on the log alpha skew normal model with geochemical applications. Appl Math 10(5):1697–1703
21.
go back to reference Sharafi M, Sajjadnia Z, Behboodian J (2017) A new generalization of alpha-skew-normal distribution. Commun Stat Theory Methods 46(12):6098–6111CrossRef Sharafi M, Sajjadnia Z, Behboodian J (2017) A new generalization of alpha-skew-normal distribution. Commun Stat Theory Methods 46(12):6098–6111CrossRef
22.
go back to reference Hazarika PJ, Shah S, Chakraborty S (2020) Balakrishnan alpha skew normal distribution: properties and applications. Malaysian J Sci 39(2):71–91CrossRef Hazarika PJ, Shah S, Chakraborty S (2020) Balakrishnan alpha skew normal distribution: properties and applications. Malaysian J Sci 39(2):71–91CrossRef
23.
go back to reference Henze N (1986) A probabilistic representation of the skew normal distribution. Scand J Statist 13:271–275 Henze N (1986) A probabilistic representation of the skew normal distribution. Scand J Statist 13:271–275
24.
go back to reference Chib S, Greenberg E (1995) Understanding the metropolis-hastings algorithm. Am Stat 49(4):327–335 Chib S, Greenberg E (1995) Understanding the metropolis-hastings algorithm. Am Stat 49(4):327–335
25.
go back to reference Cook RD, Weisberg S (1994) Transforming a response variable for linearity. Biometrika 81(4):731–737CrossRef Cook RD, Weisberg S (1994) Transforming a response variable for linearity. Biometrika 81(4):731–737CrossRef
26.
go back to reference Xiang Y, Gubian S, Suomela B, Hoeng J (2013) Generalized simulated annealing for global optimization: the GenSA package. R J 5(1):13–28CrossRef Xiang Y, Gubian S, Suomela B, Hoeng J (2013) Generalized simulated annealing for global optimization: the GenSA package. R J 5(1):13–28CrossRef
27.
go back to reference Wahed A, Ali MM (2001) The skew-logistic distribution. J Stat Res 35(2):71–80 Wahed A, Ali MM (2001) The skew-logistic distribution. J Stat Res 35(2):71–80
28.
go back to reference Nekoukhou V, Alamatsaz MH (2012) A family of skew-symmetric-Laplace distributions. Stat Pap 53(3):685–696CrossRef Nekoukhou V, Alamatsaz MH (2012) A family of skew-symmetric-Laplace distributions. Stat Pap 53(3):685–696CrossRef
29.
go back to reference Harandi SS, Alamatsaz MH (2013) Alpha–Skew–Laplace distribution. Stat Probab Lett 83(3):774–782CrossRef Harandi SS, Alamatsaz MH (2013) Alpha–Skew–Laplace distribution. Stat Probab Lett 83(3):774–782CrossRef
30.
go back to reference Hazarika PJ, Chakraborty S (2014) Alpha-skew-logistic distribution. IOSR. J Math 10(4):36–46 Hazarika PJ, Chakraborty S (2014) Alpha-skew-logistic distribution. IOSR. J Math 10(4):36–46
Metadata
Title
A Generalized-Alpha–Beta-Skew Normal Distribution with Applications
Authors
Sricharan Shah
Partha Jyoti Hazarika
Subrata Chakraborty
M. Masoom Ali
Publication date
15-04-2021
Publisher
Springer Berlin Heidelberg
Published in
Annals of Data Science / Issue 4/2023
Print ISSN: 2198-5804
Electronic ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-021-00325-0

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