{
  "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\n\n62N05; 62F15; 62E15; 68T07; 62P10.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.",
    "Department of Quantum AI, School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "P Furqan Ahmed"
    },
    {
      "affs": [
        1
      ],
      "name": "V Sujatha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8n7a52xjxs34z.bib",
  "cited_by": 0,
  "doi": "10.3389/frai.2026.1934204",
  "fulltext_url": "https://europepmc.org/articles/PMC13683756",
  "id": "8n7a52xjxs34z",
  "issns": [
    "2624-8212"
  ],
  "landing_url": "https://europepmc.org/article/MED/42909111",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7220848884",
  "pdf_url": "https://europepmc.org/articles/PMC13683756?pdf=render",
  "pmcid": "PMC13683756",
  "pmid": "42909111",
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8n7a52xjxs34z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:14Z",
      "native_id": "MED:42909111",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42909111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Distribution Estimation and Applications",
      "subfield": "statistics"
    }
  ],
  "title": "A novel Weighted Exponential-Lindley distribution with Bayesian estimation under progressive Type-II censoring and a Bayesian-Calibrated Variational Autoencoder for survival prediction.",
  "title_text": "A novel Weighted Exponential-Lindley distribution with Bayesian estimation under progressive Type-II censoring and a Bayesian-Calibrated Variational Autoencoder for survival prediction.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:14Z",
  "url": "https://research.draconitic.com/paper/8n7a52xjxs34z",
  "venue": "Frontiers in artificial intelligence",
  "versions": []
}