This paper introduces the Log-Expo Inverse Gompertz Distribution (LET-IG) three-parameter distribution and examines some of its mathematical properties. The study derives the density distribution, reliability function, and hazard rate function. It also provides ordinary moments, quantile function, mean residual life, and Renyi entropy. Five estimation methods for the LET-IG distribution based on complete sampling are discussed. A Monte Carlo simulation study is used to calculate the squared bias and variances of the estimates.
M. S. Eliwa (2019) [10] introduced and analyzed a novel three-parameter generalized model called the Kumaraswamy inverse Gompertz distribution. In 2021, M. El-Morshedy [9] developed a four-parameter lifetime model known as the exponentiated generalized inverted Gompertz distribution. In 2022, Arun [2] presented the half Cauchy inverse Gompertz distribution, which utilizes the half-Cauchy distribution as its baseline. In the same year, Moustafa [12] examined the inverse Gompertz distribution (IG) and estimated its survival function. T. M. Adegoke (2023) [13] applied the quadratic rank transmutation map scheme to derive the distribution. Additionally, Taiwo et al. (2023) [14] introduced the Topp-Leone Inverse Gompertz Distribution, an extension of the Gompertz distribution aimed at modeling lifetime datasets. Heba (2023) [4] proposed an adaptive Type-II hybrid progressive censoring strategy to enhance the effectiveness of statistical inference.