## 1 Motivation and Introduction  
In recent times, the construction of bounded distributions has grown tremendously. The unit distributions are necessary for modelling proportions, scores, rates, indices, etc. The benefit of these bounded distributions is that they allow the basic distribution to be more flexible throughout the unit interval without introducing new parameters. The well-known beta distribution is perhaps the first model that was employed for data observed in the interval (0, 1). Besides this, [PERSON]'s distribution ([PERSON] [1]) and the Topp-Leone distribution ([PERSON] and [PERSON] [2]) deserve attention. Recently, several notable models have been presented as alternatives to the beta and Kumaraswamy distributions in order to improve modelling flexibility using appropriately transformed methods. The transformation of the well-known continuous distributions has frequently been used to present the newly suggested unit distributions. The transformations of the form \(T=1/(1+X)\), \(T=X/(1+X)\), and \(T=e^{-X}\), are popularly used when \(X\) is a positive-valued random variable. Several probability distributions have been developed in this area for dealing with restricted datasets in various domains using the previous transformation. Among the most notable distributions are: unit gamma ([PERSON] [3] and [PERSON] [4]), unit logistic ([PERSON] and [PERSON] [5] and [PERSON] et al. [6]), unit Birnbaum-Saunders ([PERSON] et al. [7]), unit Weibull ([PERSON] et al. [8; 9]), unit inverse Gaussian ([PERSON] et al. [10]), unit Gompertz ([PERSON] et al. [11]), unit Lindley ([PERSON] et al. [12]), unit generalized half-normal ([PERSON] [13]), unit modified Burr-III ([PERSON] et al. [14]), unit Burr-XII (UBXII) ([PERSON] and [PERSON] [15]), unit gamma/Gompertz ([PERSON] et al. [16]), unit log-logistic ([PERSON] [17]), and unit generalized log Burr XII (UGLBXII) ([PERSON] et al. [18]). In addition to the preceding transformations, [PERSON] et al. [19] and [PERSON] et al. [20] developed a broad strategy based on the cumulative distribution function (CDF)-quantile function (QF). In a wide range of academic and professional fields, lifetime modeling and analysis are essential components of statistical work. A complete explanation of an event that only happens once in a lifetime typically follows a thorough data analysis based on a carefully chosen statistical model. The development of new probability distributions was necessary as a result of several attempts to construct models with different features. Lifetime distributions, a crucial statistical technique, can be used to model the numerous properties of lifetime datasets. These datasets can be analyzed using rather complicated distributions found in the statistical literature. One of the most-significant lifetime models is the exponentiated half-logistic distribution (EHLD). It has a number of characteristics that make it a viable alternative to well-known distributions, and at the same time, it has the ability to model various real datasets. It has been used in a variety of fields, including insurance, engineering, medical, and education. The probability density function (PDF) and CDF of the EHLD are represented by:  
\[f(y)=\frac{2\delta\varphi e^{-\delta y}}{\left(1+e^{-\delta y}\right)^{2}} \bigg{(}\frac{1-e^{-\delta y}}{1+e^{-\delta y}}\bigg{)}^{\varphi-1};\quad y, \delta,\varphi>0, \tag{1}\]  
\[F(y)=\bigg{(}\frac{1-e^{-\delta y}}{1+e^{-\delta y}}\bigg{)}^{\varphi};\quad \quad\quad y,\ \delta,\varphi>0,\]  
where \(\delta\), and \(\varphi\) are the scale and shape parameters, respectively. PDF (1) gives the half-logistic distribution (HLD) for \(\varphi=1\). The EHLD has recently caught the interest of a large number of academics. The parameters and reliability estimators of the EHLD utilizing the maximum likelihood (ML) and Bayesian techniques were examined using a progressive censoring scheme [21; 22; 23]. [PERSON] et al.