Log-Inverse Gompertz Distribution: Properties and Application to Insurance and Soil Moisture Datasets

Usman, Abubakar; Abdalla, Gaber Sallam Salem; Ehizojie, Ehinomen Emmanuel; Aliyu, Yakubu

doi:10.21608/cjmss.2025.380747.1175

Log-Inverse Gompertz Distribution: Properties and Application to Insurance and Soil Moisture Datasets

Document Type : Original Article

Authors

¹ Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria 234101, Nigeria

² Department of Insurance and Risk Management, Faculty of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

10.21608/cjmss.2025.380747.1175

Abstract

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.

Keywords