Analyzing runoff variability index in northern Thailand using length-biased Weibull-Rayleigh distribution

Tanachot Chaito; Manad Khamkong; Tanachot Chaito; Manad Khamkong

doi:10.3934/math.2025655

AIMS Mathematics

2025, Volume 10, Issue 6: 14539-14559. doi: 10.3934/math.2025655

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Analyzing runoff variability index in northern Thailand using length-biased Weibull-Rayleigh distribution

Tanachot Chaito ,
Manad Khamkong ^,

Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

Received: 19 May 2025 Revised: 15 June 2025 Accepted: 23 June 2025 Published: 26 June 2025
MSC : 62E10, 62F10, 62P12

The runoff variability index evaluates the fluctuations in runoff levels. In this article, we outline a method for quantifying the runoff variability index using the length-biased Weibull-Rayleigh (LBWR) distribution and the selecting a suitable parameter estimation technique (the maximum likelihood estimators (MLE), method of moment (MOM), maximum product of spacings estimators (MPSE), Anderson-Darling minimum distance estimators (ADE), and Cramér-von Mises minimum distance estimators (CMVE) methods). Our simulations results indicated that most ADE methods showed enhanced efficiency compared to other estimation methods in terms of mean square error (MSE) and average relative bias (AvRB). This study represents the first investigation into the runoff variability index that integrates the LBWR distribution with ADE parameter estimation. Four stations were studied: Two in Nan province and two in Phrae province. The results indicated that Nan province experiences events more frequently than once every ten years, in contrast to Phrae province. Furthermore, the runoff variability index values are useful for classifying the runoff at the four study locations, which corresponds with the particular geographic conditions at each site. Local and regional authorities can use this runoff variability index values to formulate evidence-based water management strategies, improve flood preparedness, and support long-term water security. This directly contributes to the development of more sustainable and resilient infrastructure in the face of an increasingly variable climate.
- climate change adaptation,
- length-biased Weibull-Rayleigh distribution,
- model selection,
- parameter estimation,
- return periods,
- runoff data
Citation: Tanachot Chaito, Manad Khamkong. Analyzing runoff variability index in northern Thailand using length-biased Weibull-Rayleigh distribution[J]. AIMS Mathematics, 2025, 10(6): 14539-14559. doi: 10.3934/math.2025655

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Abstract

The runoff variability index evaluates the fluctuations in runoff levels. In this article, we outline a method for quantifying the runoff variability index using the length-biased Weibull-Rayleigh (LBWR) distribution and the selecting a suitable parameter estimation technique (the maximum likelihood estimators (MLE), method of moment (MOM), maximum product of spacings estimators (MPSE), Anderson-Darling minimum distance estimators (ADE), and Cramér-von Mises minimum distance estimators (CMVE) methods). Our simulations results indicated that most ADE methods showed enhanced efficiency compared to other estimation methods in terms of mean square error (MSE) and average relative bias (AvRB). This study represents the first investigation into the runoff variability index that integrates the LBWR distribution with ADE parameter estimation. Four stations were studied: Two in Nan province and two in Phrae province. The results indicated that Nan province experiences events more frequently than once every ten years, in contrast to Phrae province. Furthermore, the runoff variability index values are useful for classifying the runoff at the four study locations, which corresponds with the particular geographic conditions at each site. Local and regional authorities can use this runoff variability index values to formulate evidence-based water management strategies, improve flood preparedness, and support long-term water security. This directly contributes to the development of more sustainable and resilient infrastructure in the face of an increasingly variable climate.

References

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