Record-based Transmuted Unit-Omega Distribution: different methods of estimation and applications: Accepted - August 2024

Ashok  Kumar Pathak; Mohd Arshad; Alok  Kumar Pandey; Alam  Ali

Authors

Ashok Kumar Pathak Central University of Punjab https://orcid.org/0000-0002-0774-1202
Mohd Arshad Indian Institute of Technology Indore https://orcid.org/0000-0002-1877-4552
Alok Kumar Pandey Central University of Punjab https://orcid.org/0009-0000-6124-6635
Alam Ali Central University of Punjab https://orcid.org/0009-0006-1273-0651

Keywords:

Omega distribution, record values, transmuted distribution, Gauss hypergeometric function, incomplete gauss hypergeometric function, estimation methods

Abstract

Dombi et al. (2019) introduced a three parameter omega distribution and showed that its asymptotic distribution is the Weibull model. We propose a new record-based transmuted generalization of the unit omega distribution by considering Balakrishnan and He (2021) approach. We call it the RTUOMG distribution. We derive expressions for some statistical quantities, like, probability density function, distribution, hazard function, quantile function, moments, incomplete moments, inverted moments, moment generating function, Lorenz curve, and Bonferroni curve of the proposed distribution. The numerical values of various measures of central tendency and coefficient of skewness and kurtosis are also presented. Concepts of stochastic ordering and some results related to ordered statistics of the RTUOMG distribution are discussed. The parameters of the RTUOMG distribution are estimated using five distinct estimators. Additionally, the Monte Carlo simulations are performed to assess the performance of these estimators. Finally, two real data sets are analyzed to demonstrate the utility of the RTUOMG distribution.