Confidence Intervals for the Coefficient of Quartile Variation of a Zero-inflated Lognormal Distribution

Noppadon Yosboonruang,Sa-Aat Niwitpong

doi:10.28991/esj-2021-01289

Noppadon Yosboonruang, Sa-Aat Niwitpong

Open Access

https://doi.org/10.28991/esj-2021-01289

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Abstract

There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PDF

Highlights

Fisheries research, which encompasses many of the natural science fields, frequently provides non-negative data following a skewed distribution [1,2,3]
We proposed approaches based on fiducial GCI (FGCI) and the Bayesian method to establish confidence intervals for the coefficient of quartile variation (CQV) of a zero-inflated lognormal distribution
Since the CQV is appropriate for extremely skewed data, the red cod data from a trawl survey was used to evaluate the performance of the proposed approaches

Summary

Introduction

Fisheries research, which encompasses many of the natural science fields, frequently provides non-negative data following a skewed distribution [1,2,3]. When trawl survey data are positively skewed with kurtosis, the coefficient of quartile variation (CQV) is a good alternative statistical tool for measuring the dispersion [9]. The results show that the bootstrap confidence intervals performed better than Bonett's approach for small sample sizes. Hannig et al [12] established the fiducial GCI (FGCI) for the ratio of the means of lognormal distributions that performs well for small sample sizes. Hasan and Krishnamoorthy [15] proposed MOVER and fiducial approaches to establish the confidence intervals for the ratio of CVs of lognormal distributions; their approaches were effective for small sample size cases. Thangjai et al [17] suggested the Bayesian approach for confidence interval construction for both a single lognormal CV and the difference between the CVs of two lognormal distributions

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