Bayesian nonparametric model for weighted data using mixture of Burr XII distributions

Soleiman  Khazaei; Soghra  Bohlourihajjar

doi:https://doi.org/10.59139/stattrans-2025-038

Bayesian nonparametric model for weighted data using mixture of Burr XII distributions

Soleiman Khazaei Department of Statistics, Razi University, Kermanshah, Iran ORCID:https://orcid.org/0000-0003-2537-9232 , Soghra Bohlourihajjar Department of Statistics, Razi University, Kermanshah, Iran ORCID:https://orcid.org/0000-0001-9803-5823 Statistics in Transition new series, vol. 26, 2025, 4, pages: 35-54 Published online: 5 December 2025 https://doi.org/10.59139/stattrans-2025-038 Citation: Khazaei S., Bohlourihajjar S., 2025. Bayesian nonparametric model for weighted data using mixture of Burr XII distributions. Statistics in Transition new series, 26(4), pp. 35-54 https://doi.org/10.59139/stattrans-2025-038

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ABSTRACT

In this paper, we develop a Bayesian nonparametric approach for analyzing weighted survival data. Specifically, we employ the Dirichlet Process Burr XII Mixture Model (DPBMM) to estimate the underlying density and survival functions when the observed data are weighted. Parameters are inferred using Markov chain Monte Carlo (MCMC) methods, and the Metropolis- Hastings algorithm is applied to obtain de-biased samples from the weighted observations. Numerical illustrations are provided using both simulated and real lifetime data, including the presence of censored observations. The performance of the proposed method is compared with classical kernel density estimates to demonstrate its flexibility in modeling complex and heavy-tailed distributions.

KEYWORDS

Bayesian nonparametric, weighted data, Dirichlet process, mixture model, Burr XII distribution, survival data.

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