A novel Weighted Exponential-Lindley distribution with Bayesian estimation under progressive Type-II censoring and a Bayesian-Calibrated Variational Autoencoder for survival prediction.
- 1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
- 2Department of Quantum AI, School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
Abstract
One-parameter lifetime models, such as the exponential and Lindley distributions, and two-parameter extensions such as the weighted Lindley distribution cannot separately control tail weight and dispersion, since a single shape parameter governs both. We address this with the Weighted Exponential-Lindley (WEL) distribution, a three-parameter model built by applying a length-biased weight to a mixture of exponential and Lindley components, with closed-form density, survival function, and an exact two-component gamma mixture representation. Using this representation and Glaser's failure-rate criterion, we prove that the WEL hazard rate is strictly increasing on its entire parameter space, with the scale parameter as its asymptotic level; the weight parameter then gives independent, tunable control over dispersion, skewness, and kurtosis are unavailable in the Lindley or weighted Lindley families. We develop maximum likelihood, method-of-moments, and Bayesian estimation under progressive Type-II censoring, validated through a Monte Carlo study across several parameter configurations and sample sizes, reporting bias, MSE, interval coverage, computation time, and convergence rates, including non-convergent method-of-moments runs rather than only successful ones. We then propose the Bayesian-Calibrated Variational Autoencoder Survival Model (BC-VAESM), whose decoder outputs individual, covariate-dependent WEL parameters, trained end-to-end via a censored negative log-likelihood. We evaluate both contributions on real, publicly available survival datasets, including censored clinical trial data and complete reliability/biological benchmarks, one chosen specifically to illustrate WEL's inability to represent bathtub hazards and one matching its increasing-hazard property. Fitting the censored datasets under an explicit right-censored likelihood, distinguished from the progressive Type-II scheme used in the Bayesian machinery, WEL is compared against an expanded set of competing one-, two-, and three-parameter lifetime models, including further weighted distributions. WEL is the best-fitting model on one dataset but is outperformed on others, and we report all outcomes without selective emphasis. In five-fold cross-validation, the BC-VAESM modestly exceeds a penalized Cox model and an otherwise identical Weibull-decoder autoencoder, though the improvement is not statistically significant at the sample size examined. Every estimate reported here comes from real, reproducible computation on real data.Msc 2020
62N05; 62F15; 62E15; 68T07; 62P10.
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BibTeX
@article{ahmed2026novel,
title = {{A novel Weighted Exponential-Lindley distribution with Bayesian estimation under progressive Type-II censoring and a Bayesian-Calibrated Variational Autoencoder for survival prediction.}},
author = {P Furqan Ahmed and V Sujatha},
journal = {Frontiers in artificial intelligence},
year = {2026},
month = oct,
doi = {10.3389/frai.2026.1934204},
url = {https://europepmc.org/article/MED/42909111},
note = {CC BY},
}
RIS
TY - JOUR
TI - A novel Weighted Exponential-Lindley distribution with Bayesian estimation under progressive Type-II censoring and a Bayesian-Calibrated Variational Autoencoder for survival prediction.
AU - P Furqan Ahmed
AU - V Sujatha
PY - 2026
DA - 2026/10/07
JO - Frontiers in artificial intelligence
DO - 10.3389/frai.2026.1934204
UR - https://europepmc.org/article/MED/42909111
AB - One-parameter lifetime models, such as the exponential and Lindley distributions, and two-parameter extensions such as the weighted Lindley distribution cannot separately control tail weight and dispersion, since a single shape parameter governs both. We address this with the Weighted Exponential-Lindley (WEL) distribution, a three-parameter model built by applying a length-biased weight to a mixture of exponential and Lindley components, with closed-form density, survival function, and an exact two-component gamma mixture representation. Using this representation and Glaser's failure-rate criterion, we prove that the WEL hazard rate is strictly increasing on its entire parameter space, with the scale parameter as its asymptotic level; the weight parameter then gives independent, tunable control over dispersion, skewness, and kurtosis are unavailable in the Lindley or weighted Lindley families. We develop maximum likelihood, method-of-moments, and Bayesian estimation under progressive Type-II censoring, validated through a Monte Carlo study across several parameter configurations and sample sizes, reporting bias, MSE, interval coverage, computation time, and convergence rates, including non-convergent method-of-moments runs rather than only successful ones. We then propose the Bayesian-Calibrated Variational Autoencoder Survival Model (BC-VAESM), whose decoder outputs individual, covariate-dependent WEL parameters, trained end-to-end via a censored negative log-likelihood. We evaluate both contributions on real, publicly available survival datasets, including censored clinical trial data and complete reliability/biological benchmarks, one chosen specifically to illustrate WEL's inability to represent bathtub hazards and one matching its increasing-hazard property. Fitting the censored datasets under an explicit right-censored likelihood, distinguished from the progressive Type-II scheme used in the Bayesian machinery, WEL is compared against an expanded set of competing one-, two-, and three-parameter lifetime models, including further weighted distributions. WEL is the best-fitting model on one dataset but is outperformed on others, and we report all outcomes without selective emphasis. In five-fold cross-validation, the BC-VAESM modestly exceeds a penalized Cox model and an otherwise identical Weibull-decoder autoencoder, though the improvement is not statistically significant at the sample size examined. Every estimate reported here comes from real, reproducible computation on real data.Msc 2020 62N05; 62F15; 62E15; 68T07; 62P10.
SN - 2624-8212
ER -