Estimation of monotone bivariate quantile inactivity time with medical applications

Mohamed Kayid; Mohamed Kayid

doi:10.3934/math.20241381

AIMS Mathematics

2024, Volume 9, Issue 10: 28472-28486. doi: 10.3934/math.20241381

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Estimation of monotone bivariate quantile inactivity time with medical applications

Mohamed Kayid ^,

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 06 August 2024 Revised: 13 September 2024 Accepted: 20 September 2024 Published: 08 October 2024
MSC : 62N01, 62N05

In most lifetime models, the bivariate $ \alpha $-quantile inactivity time is a vector of increasing functions. A novel estimator of this vector was created and investigated under this assumption. It was expected that the application of this knowledge would improve the efficiency of the estimator. It was proven that the proposed estimator is consistent and converges weakly to a bivariate Gaussian process under a suitable transformation. A simulation study was conducted to compare the performance of the proposed estimator with that of the usual estimator. Finally, the application of the proposed estimator is illustrated by analyzing a dataset comprising the time to blindness in patients with diabetic retinopathy.
- inactivity time,
- monotone bivariate quantile inactivity time,
- empirical distribution function,
- estimation
Citation: Mohamed Kayid. Estimation of monotone bivariate quantile inactivity time with medical applications[J]. AIMS Mathematics, 2024, 9(10): 28472-28486. doi: 10.3934/math.20241381

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Abstract

In most lifetime models, the bivariate $ \alpha $-quantile inactivity time is a vector of increasing functions. A novel estimator of this vector was created and investigated under this assumption. It was expected that the application of this knowledge would improve the efficiency of the estimator. It was proven that the proposed estimator is consistent and converges weakly to a bivariate Gaussian process under a suitable transformation. A simulation study was conducted to compare the performance of the proposed estimator with that of the usual estimator. Finally, the application of the proposed estimator is illustrated by analyzing a dataset comprising the time to blindness in patients with diabetic retinopathy.

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