Likelihood Inference for the Marshall–Olkin Bivariate Weibull Model with Modified Singularity Under Exact and Rounded Data
- 1Departamento de Matemáticas, Facultad de Educación y Ciencias, Universidad de Sucre, Sincelejo 700001, Colombia
- 2Departamento de Matemática y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
Abstract
The Marshall–Olkin bivariate Weibull model with modified singularity assigns positive probability to an unknown ray x=μy. We study inference for its location under exact and finite-resolution observation. With exact observations, repeated common-shock ratios permit support recovery, and conditional profiling reduces the rate-parameter optimization. With grouped observations, a rectangle likelihood retains continuous and singular mass, and a breakpoint-aware search accommodates the piecewise-smooth likelihood. In simulations with 1000 replications per scenario, the ratio of mean RMSE across four recording resolutions, comparing midpoint substitution with interval-aware estimation of μ, was approximately 29 and 39 for common-shock probabilities 0.30 and 0.50. At probability 0.10 and the coarsest resolution, 24.4% of replications met an operational weak-information criterion. A direct comparison also shows lower rate-parameter RMSE for interval-aware estimation at moderate and large singular masses, whereas shape-parameter accuracy is similar and not uniformly better. Hessian-based intervals were unavailable in many replications and their conditional coverage could be below nominal. An exploratory computational illustration with two river-response episodes demonstrates the calculations and sensitivity without supporting substantive hydrological conclusions. The study clarifies how finite recording resolution changes inference on a moving singular support and limits local uncertainty summaries.
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BibTeX
@article{brango2026likelihood,
title = {{Likelihood Inference for the Marshall–Olkin Bivariate Weibull Model with Modified Singularity Under Exact and Rounded Data}},
author = {Hugo Brango and Javier Ramirez-Montoya},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14213999},
url = {https://www.mdpi.com/2227-7390/14/21/3999},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Likelihood Inference for the Marshall–Olkin Bivariate Weibull Model with Modified Singularity Under Exact and Rounded Data
AU - Hugo Brango
AU - Javier Ramirez-Montoya
PY - 2026
DA - 2026/11/02
JO - Mathematics
DO - 10.3390/math14213999
UR - https://www.mdpi.com/2227-7390/14/21/3999
AB - The Marshall–Olkin bivariate Weibull model with modified singularity assigns positive probability to an unknown ray x=μy. We study inference for its location under exact and finite-resolution observation. With exact observations, repeated common-shock ratios permit support recovery, and conditional profiling reduces the rate-parameter optimization. With grouped observations, a rectangle likelihood retains continuous and singular mass, and a breakpoint-aware search accommodates the piecewise-smooth likelihood. In simulations with 1000 replications per scenario, the ratio of mean RMSE across four recording resolutions, comparing midpoint substitution with interval-aware estimation of μ, was approximately 29 and 39 for common-shock probabilities 0.30 and 0.50. At probability 0.10 and the coarsest resolution, 24.4% of replications met an operational weak-information criterion. A direct comparison also shows lower rate-parameter RMSE for interval-aware estimation at moderate and large singular masses, whereas shape-parameter accuracy is similar and not uniformly better. Hessian-based intervals were unavailable in many replications and their conditional coverage could be below nominal. An exploratory computational illustration with two river-response episodes demonstrates the calculations and sensitivity without supporting substantive hydrological conclusions. The study clarifies how finite recording resolution changes inference on a moving singular support and limits local uncertainty summaries.
SN - 2227-7390
ER -