Skip to main content

23.07.2024

Maximum Likelihood Estimation for Generalized Inflated Power Series Distributions

verfasst von: Robert L. Paige

Erschienen in: Annals of Data Science

Einloggen

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

search-config
loading …

Abstract

In this paper we first define the class of Generalized Inflated Power Series Distributions (GIPSDs) which contain the inflated discrete distributions most often seen in practice as special cases. We describe the hitherto unkown exponential family structure of GIPSDs and use this to derive closed-form, easy to program, conditional and unconditional maximum likelihood estimators for essentially any number of parameters. We also show how the GIPSD exponential family can be extended to model deflated mass points. Our results provide easy access to likelihood-based inference and automated model selection procedures for GIPSDs that only involve one-dimensional numerical root-finding problems that are easily solved with simple routines. We consider four real-data examples which illustrate the utility and scope of our results.

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!

Literatur
1.
Zurück zum Zitat Shi Y (2022) Advances in big data analytics theory. Algorithm and Practice, Springer, SingaporeCrossRef Shi Y (2022) Advances in big data analytics theory. Algorithm and Practice, Springer, SingaporeCrossRef
2.
Zurück zum Zitat Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York
3.
Zurück zum Zitat Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, BerlinCrossRef Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, BerlinCrossRef
4.
Zurück zum Zitat Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Annal Data Sci 4(2):149–178CrossRef Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Annal Data Sci 4(2):149–178CrossRef
5.
Zurück zum Zitat Noack A (1950) A class of random variables with discrete distributions. Ann Math Stat 21(3):127–132CrossRef Noack A (1950) A class of random variables with discrete distributions. Ann Math Stat 21(3):127–132CrossRef
6.
Zurück zum Zitat Johnson NL, Kemp AW, Kotz S (2005) Discrete univariate distributions. J Stat Plan Inference 140:2255–2259 Johnson NL, Kemp AW, Kotz S (2005) Discrete univariate distributions. J Stat Plan Inference 140:2255–2259
7.
Zurück zum Zitat Silva RB, Cordeiro G (2015) The Burr XII power series distributions: a new compounding family. Braz J Probab Stat 29:565–589CrossRef Silva RB, Cordeiro G (2015) The Burr XII power series distributions: a new compounding family. Braz J Probab Stat 29:565–589CrossRef
8.
Zurück zum Zitat Kemp AW (2010) Families of power series distributions, with particular reference to the lerch family. J Stat Plan Inference 140:2255–2259CrossRef Kemp AW (2010) Families of power series distributions, with particular reference to the lerch family. J Stat Plan Inference 140:2255–2259CrossRef
9.
Zurück zum Zitat Gupta PL, Gupta RC, Tripathi RC (1995) Inflated modified power series distributions with applications. Commun Stat Theory Methods 24(9):2355–2374CrossRef Gupta PL, Gupta RC, Tripathi RC (1995) Inflated modified power series distributions with applications. Commun Stat Theory Methods 24(9):2355–2374CrossRef
10.
Zurück zum Zitat Murat M, Szynal D (1998) Non-zero inflated modified power series distributions. Commun Stat Theory Methods 27(12):3047–3064CrossRef Murat M, Szynal D (1998) Non-zero inflated modified power series distributions. Commun Stat Theory Methods 27(12):3047–3064CrossRef
11.
Zurück zum Zitat Rahman T, Hazarika PJ, Barman MP (2021) One inflated binomial distribution and its real-life applications. Indian J Sci Technol 14(22):1839–1854CrossRef Rahman T, Hazarika PJ, Barman MP (2021) One inflated binomial distribution and its real-life applications. Indian J Sci Technol 14(22):1839–1854CrossRef
12.
Zurück zum Zitat Alshkaki RSA (2016) On the zero-one inflated poisson distribution. Int J Stat Distrib Appl 2(4):42–48 Alshkaki RSA (2016) On the zero-one inflated poisson distribution. Int J Stat Distrib Appl 2(4):42–48
14.
15.
Zurück zum Zitat Lehmann EL, Casella G (1998) Theory of point estimation, 2nd edn. Springer-Verlag, New York Lehmann EL, Casella G (1998) Theory of point estimation, 2nd edn. Springer-Verlag, New York
16.
Zurück zum Zitat Dietz E, Bohning D (2000) On estimation of the Poisson parameter in zero-modified Poisson models. Comput Stat Data Anal 34(4):441–459CrossRef Dietz E, Bohning D (2000) On estimation of the Poisson parameter in zero-modified Poisson models. Comput Stat Data Anal 34(4):441–459CrossRef
17.
Zurück zum Zitat Rahman T, Hazarika PJ, Ali MM, Barman MP (2022) Three-inflated poisson distribution and its application in suicide cases of india during Covid-19 pandemic. Ann Data Sci 9(5):1103–1127CrossRef Rahman T, Hazarika PJ, Ali MM, Barman MP (2022) Three-inflated poisson distribution and its application in suicide cases of india during Covid-19 pandemic. Ann Data Sci 9(5):1103–1127CrossRef
18.
Zurück zum Zitat Kumar CS, Riyaz A (2013) On the zero-inflated logarithmic series distribution and its modification. Statistica 73:477–492 Kumar CS, Riyaz A (2013) On the zero-inflated logarithmic series distribution and its modification. Statistica 73:477–492
19.
Zurück zum Zitat Greenwood M, Yule GU (1920) An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J R Stat Soc 83(2):255–279CrossRef Greenwood M, Yule GU (1920) An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J R Stat Soc 83(2):255–279CrossRef
20.
Zurück zum Zitat Bohning D, Ekkehart D, Schlattmann P, Mendonca L, Kircher U (1999) The zero-inflated poisson model and the decayed. Missing and filled teeth index in dental epidemiology. J R Stat Soc A 162(2):195–209CrossRef Bohning D, Ekkehart D, Schlattmann P, Mendonca L, Kircher U (1999) The zero-inflated poisson model and the decayed. Missing and filled teeth index in dental epidemiology. J R Stat Soc A 162(2):195–209CrossRef
Metadaten
Titel
Maximum Likelihood Estimation for Generalized Inflated Power Series Distributions
verfasst von
Robert L. Paige
Publikationsdatum
23.07.2024
Verlag
Springer Berlin Heidelberg
Erschienen in
Annals of Data Science
Print ISSN: 2198-5804
Elektronische ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-024-00560-1

Premium Partner