## 1 Introduction  
Ref. [1] investigated the characteristics of the Lindley distribution (LD) in great depth. According to [2], there are some circumstances in which the LD may not be appropriate from a theoretical or applied point of view. Due to this, ref. [2] introduced the power Lindley (PL) distribution, a more adaptable distribution, using a power transformation method. Ref. [2] showed that based on the values of the parameters, the hazard function of the PL distribution can rise, decrease, or decrease-increase-decrease. Some of the other distributions that have been suggested utilizing the power transformation method are the power Shanker distribution by [3], the power Ishita and Aradhana distributions by [4], and the power Rama and Garima distributions by [5,6]. The power Ishita distribution is proposed by [7], the power Sujatha distribution is considered by [8], and the power Prakaamy distribution is proposed by [9]. In addition, ref. [10] suggested the power half-logistic distribution, ref. [11] introduced the power binomial exponential distribution, ref. [12] proposed the power length-biased Suja distribution, ref. [13] discussed a novel three-parameter distribution known as the power Dama distribution (PDD), ref. [14] offered the power XLindley distribution, and ref. [15] proposed the power-modified Kiese-exponential distribution. All of the power-transformed distributions are shown to be more adaptable than their respective baseline distributions, and more effective for analyzing complicated data structures in various spheres of life. Ref. [16] provided a novel lifetime distribution with one parameter for modeling lifetime data from engineering and medical science, known as Zeghdoudi distribution (ZD), with a cumulative distribution function (cdf) given by  
\[F(y;\theta)=1-\bigg{(}1+\frac{\theta^{2}y^{2}+\theta(\theta+2)y}{2+\theta}\bigg{)} e^{-\theta y},\quad y>0,\theta>0, \tag{1}\]  
and a survival function defined as  
\[S(y;\theta)=1-F(y;\theta)=\bigg{(}1+\frac{\theta^{2}y^{2}+\theta(\theta+2)y}{ 2+\theta}\bigg{)}e^{-\theta y}.\]  
The probability density function (pdf) of the ZD is  
\[f(y;\theta)=\frac{\theta^{3}}{2+\theta}y(1+y)e^{-\theta y},\quad y>0,\theta>0,\]  
and its hazard function has the form  
\[h(y;\theta)=\frac{f(y,\theta)}{1-F(y,\theta)}=\frac{\theta^{3}y(1+y)}{2+ \theta+\theta^{2}y^{2}+\theta(\theta+2)y}.\]  
The ZD has the mean \(E(Y)=\frac{2(\theta+3)}{\theta(\theta+2)}\), variance \(Var(Y)=\frac{2\big{(}\theta^{2}+\theta\theta+6\big{)}}{\theta^{2}(2+\theta)^ {2}}\), coefficient of skewness \(SK=\frac{24(\theta+5)(\theta+2)^{2}}{(2\theta^{2}+12\theta+12)^{2}}\), and coefficient of kurtosis \(Ku=\frac{30(\theta+6)(\theta+2)^{3}}{(\theta^{2}+6\theta+6)^{6}}\). According to [16], the maximum likelihood (MLE) and method of moment (MOM) estimators of the distribution parameter have the same forms as  
\[\hat{\theta}_{\text{MOM}}=\theta_{\text{MLE}}=\frac{1}{y}\bigg{(}1-\overline{ y}+\sqrt{\overline{y}^{2}+4\overline{y}+1}\bigg{)}\]  
where \(\overline{y}=\frac{1}{n}\sum\limits_{i=1}^{n}y_{i}\). The accuracy of the parametric distributions is tested using several statistical methods. Numerous fresh initiatives are investigated to address these problems. Based on the well-known Kaplan and Meyer estimators, refs. [17; 18] recommended a new form of the Chi-squared test for randomly censored actual data. Then, for the accelerated loss distributions, ref. [19] assumed certain nonparametric adjustments for the Kolmogorov-Smirnov statistic (KSS), Anderson-Darling statistic (ADS), and Cramer-von Mises statistic (KVMS). A different Chi-squared GOF test statistic is recently presented and demonstrated by [20] for the correct censored data. For distributional validation using right-censored approaches, Bagdonavicius and Nikulin's (B-N) is the most current Chi-squared GOF test statistic in use. The B-N GOF test and a new modified Chi-square GOF test are both utilized in this research to provide a censored maximum likelihood estimation for the right-censored validation.