Confidence intervals for the difference between coefficients of variation of zero-inflated gamma distributions

Hongping Guo; Yuhang Qian; Yiran Zhu; Xinming Dai; Xiao Wang; Hongping Guo; Yuhang Qian; Yiran Zhu; Xinming Dai; Xiao Wang

doi:10.3934/math.20231521

AIMS Mathematics

2023, Volume 8, Issue 12: 29713-29733. doi: 10.3934/math.20231521

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Research article

Confidence intervals for the difference between coefficients of variation of zero-inflated gamma distributions

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
2.
Department of Applied Statistics, Social Science and Humanities, New York University, New York 10003, United States
3.
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China

Received: 09 August 2023 Revised: 21 October 2023 Accepted: 30 October 2023 Published: 02 November 2023
MSC : 62F25, 62P12

The problem of constructing confidence intervals (CIs) for the difference between coefficients of variation of two zero-inflated gamma distributions was considered. As gamma distribution does not have closed form maximum likelihood estimators, the parameters of gamma distribution have to be estimated numerically. To this end, we proposed here four different generalized confidence intervals (GCIs) based on fiducial inference, Box-Cox transformation, parametric bootstrap and the method of variance of estimates recovery (MOVER). Performances of the four GCIs were evaluated and compared via extensive simulation. The simulation results showed that all four methods returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes.
- confidence interval,
- zero-inflated gamma distribution,
- coefficient of variation,
- rainfall data
Citation: Hongping Guo, Yuhang Qian, Yiran Zhu, Xinming Dai, Xiao Wang. Confidence intervals for the difference between coefficients of variation of zero-inflated gamma distributions[J]. AIMS Mathematics, 2023, 8(12): 29713-29733. doi: 10.3934/math.20231521

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Abstract

The problem of constructing confidence intervals (CIs) for the difference between coefficients of variation of two zero-inflated gamma distributions was considered. As gamma distribution does not have closed form maximum likelihood estimators, the parameters of gamma distribution have to be estimated numerically. To this end, we proposed here four different generalized confidence intervals (GCIs) based on fiducial inference, Box-Cox transformation, parametric bootstrap and the method of variance of estimates recovery (MOVER). Performances of the four GCIs were evaluated and compared via extensive simulation. The simulation results showed that all four methods returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes.

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