Structural Characterization and Inference for an Odds-Scale Lomax Model with Applications to Unit-Interval Data

This paper develops a structural, inferential, and computational study of a Lomax-based model on a unit interval obtained through the odds transformation $Z=Y/(1+Y)$ of a baseline Lomax random variable. Rather than proposing a genuinely new unit distribution, the paper clarifies the model’s exact position in the literature by showing that it is equivalent, up to complementation and reparametrization, to a previously reported unit-Lomax-type construction. The contribution is therefore focused on its odds-scale interpretation, analytical tractability, and reliable inference. We derive the main distributional functions, endpoint behavior, hazard shapes, quantiles, moments, and odds-scale representations. We also show that likelihood inference reduces to classical Lomax inference on the odds-transformed sample, which explains the severe maximum likelihood estimator instability observed in small-sample and heavy-tailed regimes. To address this issue, we complement maximum likelihood estimation with maximum product of spacings estimation. Monte Carlo experiments and real-data applications illustrate that the maximum likelihood estimator may be reliable for moderate tail behavior and sufficiently large samples, whereas the MPS estimator provides a more stable alternative in challenging finite-sample settings.