The Wrapped New XLindley Distribution under Right Censoring: Theory, Estimation, and Applications

The Wrapped New XLindley Distribution

Abstract

This paper develops a unified likelihood-based framework for modeling right-censored circular
data using the Wrapped New XLindley Distribution (WNXLD), extending Lindley-type life-
time models to periodic domains where directional measurements are incompletely observed.
Starting from the linear New XLindley distribution, we construct its wrapped counterpart,
derive closed-form expressions for the density, survival, and censored likelihood functions,
and obtain score equations for maximum likelihood estimation. Asymptotic properties of the
estimator are discussed under standard regularity conditions, and stable numerical optimiza-
tion strategies are proposed for practical implementation. Extensive Monte Carlo simulations
evaluate bias, efficiency, robustness to censoring, and truncation effects in the infinite-series
representation. Applications to wind direction and animal movement data demonstrate that
the WNXLD provides superior fit compared with commonly used wrapped distributions,
particularly when circular data exhibit asymmetry or multimodality. The proposed model
therefore offers a flexible and computationally tractable tool for circular survival analysis in
environmental, biological, and reliability studies.