Record-based transmuted unit omega distribution: different methods of estimation and applications

TL;DR

This paper introduces a new record-based transmuted unit omega distribution (RTUOMG), deriving its properties, estimating its parameters with five methods, and demonstrating its applicability through simulations and real data analysis.

Contribution

It proposes the RTUOMG distribution, a novel generalization of the omega distribution, with comprehensive theoretical properties and practical estimation techniques.

Findings

Derived explicit formulas for statistical measures of RTUOMG.

Evaluated estimator performance via Monte Carlo simulations.

Applied RTUOMG to real datasets demonstrating its usefulness.

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.