Confidence Intervals for the Mean of Lognormal Data with Excess Zeros

Tian, Lili; Wu, Jianrong

doi:10.1002/bimj.200510155

Cited by 40 publications

(20 citation statements)

References 11 publications

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“…Land [24,26,27], Mohn [23], Angus [28], Zhou and Gao [25], Zhou and Tu [29], Tian and Wu [30], among others. Procedures that give optimum confidence interval for finite samples are difficult to compute.…”

Section: Proposed Confidence Interval For the True Meanmentioning

confidence: 97%

Statistical analysis and modeling of coral reef habitats

Hoare

Tsokos

2009

Nonlinear Analysis: Theory, Methods & Applications

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Section: Proposed Confidence Interval For the True Meanmentioning

confidence: 97%

Statistical analysis and modeling of coral reef habitats

Hoare

Tsokos

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…Aitchison & Brown (1963) first introduced the delta-lognormal distribution for non-negative data containing zero values with the probability 0 < δ < 1; positive observations with the remainder of the probability 1 − δ follow a lognormal distribution and the zeros follow a binomial distribution with binomial proportion δ. The delta-lognormal distribution has been fitted for real-world examples in many research areas such as the environment (Owen & DeRouen, 1980;Hasan & Krishnamoorthy, 2018), fishery surveys (Pennington, 1983;Smith, 1988Smith, , 1990Lo, Jacobson & Squire, 1992;Fletcher, 2008;Wu & Hsieh, 2014) and medicine (Zhou & Tu, 1999, 2000Tian & Wu, 2006;Hasan & Krishnamoorthy, 2018).…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand

Maneerat¹,

Niwitpong²,

Niwitpong³

2020

PeerJ

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Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

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“…Tian (2005) compared the generalized variables method and the generalized pivotal quantity (GPQ) to construct confidence intervals for the mean, between which the generalized variables method was preferable. Tian & Wu (2006) recommended using the adjusted signed log-likelihood ratio statistic to construct confidence intervals for the mean. Chen & Zhou (2006) considered interval estimations for the ratio of or difference between two means using a true generalized pivotal (GP) method, an approximate GP method, a signed log-likelihood ratio method, and a modified signed log-likelihood ratio method; their results show that the approximate GP method performed the best.…”

Section: Introductionmentioning

confidence: 99%

The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

Yosboonruang¹,

Niwitpong²,

Niwitpong³

2020

PeerJ

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The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.

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Confidence Intervals for the Mean of Lognormal Data with Excess Zeros

Cited by 40 publications

References 11 publications

Statistical analysis and modeling of coral reef habitats

Statistical analysis and modeling of coral reef habitats

A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand

The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

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