• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

Article

One Inflated Binomial Distribution and its Real-Life Applications
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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v14i22.404

Year: 2021, Volume: 14, Issue: 22, Pages: 1839-1854

Original Article

One Inflated Binomial Distribution and its Real-Life Applications

Tousifur Rahman1 , Partha Jyoti Hazarika1 , Manash Pratim Barman​ ✉ 1

1 Department of Statistics, Dibrugarh University, Dibrugarh, Assam, 786004, India

email: [email protected]

Received Date:02 April 2021, Accepted Date:27 May 2021, Published Date:29 June 2021

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: To introduce a one-inflated Binomial distribution (OIBD) and discuss its applications. Methods: Study its distributional properties, reliability characteristics, and estimation of its parameters using the method of moment estimation (MM) and maximum likelihood estimation (MLE). A simulation study has been conducted to see the behaviour of the MLEs. Two real-life examples are used to examine the pertinent of the proposed distribution. Findings : The proposed one-inflated binomial distribution (OIBD) provides better fitting in terms of AIC, BIC, and KS test comparison to the other known distributions. Novelty: Develop a new statistical distribution to study the count data having inflated frequency at count one, along with the different statistical properties. The practical utility of the distribution is also discussed with real-life examples.

Keywords

One inflated Binomial distribution, MM, MLE, KS, AIC and BIC

References

  1. Mallick A, Joshi R. Parameter Estimation and Application of Generalized Inflated Geometric Distribution. Journal of Statistical Theory and Applications. 2018;17(3):491–519. Available from: https://dx.doi.org/10.2991/jsta.2018.17.3.7
  3. Winai B, Siriporn S, Prasit P. The zero-inflated negative binomial-Erlang distribution: An application to highly pathogenic avian influenza H5N1 in Thailand. Songklanakarin Journal of Science and Technology. 2018;40(6):1428–1436. Available from: https://rdo.psu.ac.th/sjstweb/journal/40-6/24.pdf
  4. Neyman J. On a New Class of "Contagious" Distributions, Applicable in Entomology and Bacteriology. The Annals of Mathematical Statistics. 1939;10(1):35–57. Available from: https://dx.doi.org/10.1214/aoms/1177732245
  5. Feller W. On a General Class of "Contagious" Distributions. The Annals of Mathematical Statistics. 1943;14(4):389–400. Available from: https://dx.doi.org/10.1214/aoms/1177731359
  6. Gupta PL, Gupta RC, Tripathi RC. Inflated modified power series distributions with applications. Communications in Statistics - Theory and Methods. 1995;24(9):2355–2374. Available from: https://dx.doi.org/10.1080/03610929508831621
  7. Murat M, Szynal D. Non–zero inflated modified power series distributions. Communications in Statistics - Theory and Methods. 1998;27(12):3047–3064. Available from: https://dx.doi.org/10.1080/03610929808832272
  12. Beckett S, Jee J, Ncube T, Pompilus S, Washington Q, Singh A, et al. Zero-inflated Poisson (ZIP) distribution: parameter estimation and applications to model data from natural calamities. Involve, a Journal of Mathematics. 2014;7:751–767. Available from: https://dx.doi.org/10.2140/involve.2014.7.751
  13. Nanjundan G, Sadik P. A characterization of Zero-inflated binomial model. International journal of mathematics and computer research. 2015;3(10):1188–1190. Available from: https://ijmcr.in/index.php/ijmcr/article/view/142
  14. Suresh R, Nanjundan G, Nagesh S, Pasha S. On a Characterization of Zero-Inflated Negative Binomial Distribution. Open Journal of Statistics. 2015;05(06):511–513. Available from: https://dx.doi.org/10.4236/ojs.2015.56053
  15. Nanjundan G, Pasha S. A Note on the Characterization of Zero-Inflated Poisson Model. Open Journal of Statistics. 2015;05(02):140–142. Available from: https://dx.doi.org/10.4236/ojs.2015.52017
  16. Abdulrazak ARS. On the Zero-One Inflated Poisson distribution. International journal of Statistical Distributions and Applications. 2016;2(4):42–48. Available from: https://doi.org/10.11648/j.ijsd.20160204.11
  17. Mwalili SM, Lesaffre E, Declerck D. The zero-inflated negative binomial regression model with correction for misclassification: an example in caries research. Statistical Methods in Medical Research. 2008;17(2):123–139. Available from: https://dx.doi.org/10.1177/0962280206071840
  19. Sakthivel KM, Rajitha C. Estimation of Zero-Inflation Parameter in Zero-Inflated Poisson Model. International Journal of Mathematics Trends and Technology. 2018;56(2):135–140. Available from: https://doi.org/10.14445/22315373/IJMTT-V56P519
  20. Jornsatian C, Bodhisuwan W. Zero-one inflated negative binomial - beta exponential distribution for count data with many zeros and ones. Communications in Statistics - Theory and Methods. 2021;p. 1–15. Available from: https://dx.doi.org/10.1080/03610926.2021.1898642
  21. Sheldon R. Simulation. Elsevier Academic Press. 2012.
  25. Malhotra A, Vanneman R, Kishor S. Fertility, Dimensions of Patriarchy, and Development in India. Population and Development Review. 1995;21(2):281–305. Available from: https://dx.doi.org/10.2307/2137495
  26. Kulkarni PM. Gender preference contraceptive prevalence: Evidence of regional variations. Economic and Political Weekly. 1999;34(42-43):3058–3062. Available from: https://www.jstor.org/stable/4408537
  27. Arvind KS, Yadava R, Tiwari AK. Measuring Son Preference Through Number of Children Born. Demography India. 2018;47(2):67–82. Available from: http://demographyindia.in/article_document/73/817706.pdf
  28. Kenneth PB, David RA. Multimodel inference: understanding AIC and BIC in Model Selection. Sociological Methods & Research. 2004;33(2):261–304. Available from: https://doi.org/10.1177/0049124104268644

Copyright

© 2021 Rahman et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)

  • 29 June 2021

Year: 2021, Volume: 14, Issue: 22

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