Skip to main content
Erschienen in:

15.04.2021

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

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

Erschienen in: Annals of Data Science | Ausgabe 4/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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
Metadaten
Titel
A Generalized-Alpha–Beta-Skew Normal Distribution with Applications
verfasst von
Sricharan Shah
Partha Jyoti Hazarika
Subrata Chakraborty
M. Masoom Ali
Publikationsdatum
15.04.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Annals of Data Science / Ausgabe 4/2023
Print ISSN: 2198-5804
Elektronische ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-021-00325-0

Premium Partner