A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications

Authors

  • Anum Shafiq
  • Tabassum Naz Sindhu
  • Zawar Hussain
  • Josmar Mazucheli Universidade Estadual de Maringá
  • Bruna Alves Universidade Estadual de Maringá

DOI:

https://doi.org/10.17713/ajs.v52i2.1407

Abstract

In explaining and forecasting real life scenarios, statistical distributions are very helpful. It is very important to select the best fitting statistical distribution for modelling data. In analysis of real world phenomena like in reliability and economics, we may find
distributions for bounded data observed as percentages, proportions or fractions (see, for example, Marshall and Olkin (2007)). In this context, in view of pertinent transformation on the Gumbel Type-II model, we suggest and study the unit Gumbel Type-II (UG-TII)
model and explore few of its statistical characteristics. We also consider various methods of estimating the unknown parameters of UG-TII model from the frequentist perspective. Monte Carlo simulations are worked out in order to compare efficiency of suggested
estimation methods for small as well as large samples. The efficiency of estimators is measured using simulated samples in terms of their bias and mean square error. In the end, two datasets have been examined in attempt to validate the realistic possibilities of
new model. In comparison to the six severe competitors.

Downloads

Published

2023-03-12

How to Cite

Shafiq, A., Sindhu, T. N., Hussain, Z., Mazucheli, J., & Alves, B. (2023). A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications. Austrian Journal of Statistics, 52(2), 116–140. https://doi.org/10.17713/ajs.v52i2.1407

Issue

Vol. 52 No. 2 (2023): Regular Issue

Section

Articles

License

Copyright (c) 2023 Anum Shafiq, Tabassum Naz Sindhu, Zawar Hussain, Josmar Mazucheli, Bruna Alves

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. 

The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.

Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.

 

Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.