Kumaraswamy-Teissier Distribution: Bayesian and Non-Bayesian Inference, Regression Modeling and Climate Application
Abstract
This study introduces the three-parameter Kumaraswamy--Teissier distribution (KTD) by applying the Kumaraswamy-G construction to the Teissier distribution. The proposed distribution provides additional shape flexibility for modelling positive-valued observations and accommodates different density and hazard-rate shapes. Several statistical properties, including moments, the moment generating function, quantile function, and order statistics, are derived. Maximum likelihood, maximum product spacing, and Bayesian methods are considered for parameter estimation, and simulation results demonstrate improving estimation accuracy with increasing sample size. A median-based regression model is further developed for the KTD, with its finite-sample performance examined through simulation. The practical utility of the proposed regression model is demonstrated through an application to monthly gridded rainfall data from the Northwest Himalayas, incorporating annual and semi-annual harmonic terms to capture seasonal variation. Its performance is assessed against Kumaraswamy and beta regression using residual-based goodness-of-fit diagnostics and likelihood-based model selection. The results demonstrate effectiveness of the proposed distribution for modelling heterogeneous and skewed positive-valued rainfall data.
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BibTeX
@misc{mishra2026kumaraswamyteissier,
title = {{Kumaraswamy-Teissier Distribution: Bayesian and Non-Bayesian Inference, Regression Modeling and Climate Application}},
author = {Kamana Mishra and Neeraj Poonia and Tanmay Kayal and Sarita Azad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00060},
eprint = {2610.00060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00060},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kumaraswamy-Teissier Distribution: Bayesian and Non-Bayesian Inference, Regression Modeling and Climate Application
AU - Kamana Mishra
AU - Neeraj Poonia
AU - Tanmay Kayal
AU - Sarita Azad
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.00060
UR - https://arxiv.org/abs/2610.00060
AB - This study introduces the three-parameter Kumaraswamy--Teissier distribution (KTD) by applying the Kumaraswamy-G construction to the Teissier distribution. The proposed distribution provides additional shape flexibility for modelling positive-valued observations and accommodates different density and hazard-rate shapes. Several statistical properties, including moments, the moment generating function, quantile function, and order statistics, are derived. Maximum likelihood, maximum product spacing, and Bayesian methods are considered for parameter estimation, and simulation results demonstrate improving estimation accuracy with increasing sample size. A median-based regression model is further developed for the KTD, with its finite-sample performance examined through simulation. The practical utility of the proposed regression model is demonstrated through an application to monthly gridded rainfall data from the Northwest Himalayas, incorporating annual and semi-annual harmonic terms to capture seasonal variation. Its performance is assessed against Kumaraswamy and beta regression using residual-based goodness-of-fit diagnostics and likelihood-based model selection. The results demonstrate effectiveness of the proposed distribution for modelling heterogeneous and skewed positive-valued rainfall data.
ER -