Unit-bounded distributions are often used to mimic values that are strictly defined inside the interval (0, 1). Despite this, these distributions are more uncommon than those with semi-bounded support (0, ∞). However, many real-life circumstances involve observations with a unit-bounded range, such as proportions, percentages, ratios, rates, and fractions. This study introduces the Log-Inverse Gompertz Distribution (LIGD), derived via a negative exponential transformation of the Inverse Gompertz distribution. The LIGD exhibits flexible density shapes (J, reversed-J, and left-skewed unimodal) and a strictly increasing hazard rate. The study examines statistical aspects and reliability measures such as survival, hazard, cumulative hazard, reversal hazard, quantile functions, median, skewness, kurtosis, and order statistics. The parameters of the proposed model were estimated using maximum likelihood estimation and maximum product of spacing, with a Monte Carlo simulation utilized to assess the efficacy of various estimating approaches. Finally, the proposed model's applicability is illustrated using two real-world data sets. A comparative analysis demonstrates that the proposed model outperforms many existing ones.