###### Abstract  
This article discusses different methods for estimating the shape and scale parameters of the generalized inverted exponential distribution (GIED) and the acceleration factor in constant stress partially accelerated life test (CSPALT) with general progressively Type-II censored samples. We obtain the maximum likelihood estimates for the three parameters and calculate correlated approximate confidence intervals. Bayesian point estimates and credible intervals are also determined using the importance sampling method. Monte-Carlo simulation studies are conducted to demonstrate and compare the effectiveness of the proposed parameter estimation techniques. Additionally, a real-life dataset is examined to highlight the practical utility of these methodologies. Our findings indicate that the GIED provides an appropriate and flexible model for the real lifetime data, and the Bayesian approach offers better estimation than classical methods under most scenarios, in terms of using generally progressively Type-II censored samples under CSPALT. general progressive Type-II censoring; general inverted exponential distribution; constant stress partially accelerated life test; maximum likelihood estimation; Bayesian estimation; importance sampling +
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where \(\lambda,\alpha>0\) are called the scale and shape parameter separately. It is worth noting that when \(\alpha=1\), GIED is simplified to a special case: IED. Figure 1 displays various curves illustrating PDF, CDF, SF, and HRF of GIED, featuring \(\lambda=1\) (the scale parameter) across different scenarios featuring distinct values for \(\alpha\), namely the shape parameter. Compared with the exponential distribution with a constant hazard rate function, GIED features a versatile hazard rate function, the value of which varies according to the parameter \(\alpha\), see [3]. Different works were presented on GIED, ref. [4] considered the maximum likelihood estimation of the two parameters involved and derived reliability and failure rate functions under progressively type II censoring scheme in view of time cost. Ref. [5] obtained estimation of the parameters of GIED from both classical and Bayesian views and discussed a method of obtaining the optimum hybrid censoring scheme. Ref. [6] proposed a two-stage group acceptance sampling plan for generalized inverted exponential distribution under truncated life test. As technology advances, modern products are becoming more reliable and have longer lifetimes. This makes it difficult for experimenters to conduct tests that accurately determine the actual lifetime of the products within a reasonable time frame. To solve this issue, accelerated life test (ALT) has been devised as an option. These tests subject the units to more extreme conditions than normal, such as higher pressure, temperature, voltage, etc., in order to expedite failure. There are various models under accelerated life tests (ALTs) according to different ways how the stress is exerted. In a constant stress model, all the products endure an unvarying stress level until the experiment concludes or all the units fail. This type of model has been thoroughly investigated by numerous scholars. For example, ref. [7] developed a constant stress ALT model for data that follows the Lindley distribution, while ref. [8] developed a constant stress model for exponential and Weibull data to predict how much time could the products remain. In contrast, with a step stress model, the stress level changes at specific times or when a designated number of  
Figure 1: Visualization of GIED characteristics with varying \(\alpha\) and fixed \(\lambda=1\). units fail. As a result, the stress on all the products increases gradually according to some type of rule. Many authors have extensively researched the step stress models. For recent literature on this topic, ref. [9] provided a procedure of determining optimal designs of simple step-stress accelerated life tests. Ref.