In this article, we introduce and study the truncated inverse power Lindley distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Lindley distribution to the interval [0,1]. The corresponding probability density function has the potential to be unimodal, decreasing, right-skewed, and heavy-tailed. On the other hand, the hazard rate function can be increasing, N-shaped, or U-shaped. These shapes’ versatility enables accurate representation and analysis of proportional or percentage data across a wide range of applications, such as survival analysis, reliability, and uncertainty modeling. Several statistical features, such as the mode, quantiles, Bowley’s skewness, Moor’s kurtosis, MacGillivray’s skewness, moments, inverse moments, incomplete moments, and probability-weighted moments, are computed. In practice, for the estimation of the model parameters from truncated data under the progressively type-II censoring scheme, the maximum likelihood, maximum product spacing, and Bayesian approaches are used. The Tierney–Kadane approximation and Markov chain Monte Carlo techniques are employed to produce the Bayesian estimates under the squared error loss function. We present some simulation results to evaluate these approaches. Four applications based on real-world datasets—one of them is on times of infection, the second is on failure times, and the other two are on the rate of inflation in Asia and Africa—explain the significance of the new truncated model in comparison to some reputed comparable models, such as the inverse power Lindley, Kumaraswamy, truncated power Lomax, beta, truncated Weibull, unit-Weibull, Kumaraswamy Kumaraswamy, and exponentiated Kumaraswamy models.
