Confidence intervals for the mean and a percentile based on zero-inflated lognormal data

Hasan, Sazib; Krishnamoorthy, K.

doi:10.1080/00949655.2018.1439033

Cited by 34 publications

(61 citation statements)

References 25 publications

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“…The former develops the NG prior to obtain the posterior density, while the latter is an extension of Hasan and Krishnamoorthy's MOVER (Hasan & Krishnamoorthy, 2018). Both were compared with the existing CIs HPD-Jef and HPD-Rul of Harvey & Van der Merwe (2012), GCI of Wu & Hsieh (2014), and FGCI of Hasan & Krishnamoorthy (2018). Two simulation studies were conducted to show the aforementioned CI performances under equal and unequal sample sizes in different situations: S1.…”

Section: Resultsmentioning

confidence: 99%

“…Here X ij ∼ Δ(m i , σ 2 i , δ i ) is considered. Hasan & Krishnamoorthy (2018) showed the FGPQs of m i and σ 2 i as…”

Section: Fgcimentioning

confidence: 99%

“…This interval is expanded from CIs for delta-lognormal mean of Hasan & Krishnamoorthy (2018) to the ratio of delta-lognormal variances. Given the individual CIs for the parameters of interest γ, the MOVER concept is used to establish a CI for a linear combination of parameters, proposed by Krishnamoorthy & Oral (2017).…”

Section: Mover Intervalmentioning

confidence: 99%

“…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%

“…Clearly, there is a need for research that investigates and constructs CIs for the ratio of delta-lognormal variances using the highest posterior density based on normal-gamma prior (HPD-NG) and MOVER. These proposed CIs were compared with the existing HPD-based Jeffreys' (HPD-Jef) and Jeffreys' Rule (HPD-Rul) priors of Harvey & Van der Merwe (2012), GCI of Wu & Hsieh (2014) and fiducial GCI (FGCI) of Hasan & Krishnamoorthy (2018).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Here X ij ∼ Δ(m i , σ 2 i , δ i ) is considered. Hasan & Krishnamoorthy (2018) showed the FGPQs of m i and σ 2 i as…”

Section: Fgcimentioning

confidence: 99%

Section: Mover Intervalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Maneerat¹,

Niwitpong²,

Niwitpong³

2020

PeerJ

View full text Add to dashboard Cite

show abstract

Bayesian confidence intervals for the difference between variances of delta‐lognormal distributions

Maneerat

Niwitpong

2020

Biometrical J

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Tolerance limits under zero‐inflated lognormal and gamma distributions

Zimmer

Park

Mathew

2020

Comp and Math Methods

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The computation of upper tolerance limits is investigated for the zero‐inflated lognormal distribution and the zero‐inflated gamma distribution, with or without covariates. The methodologies investigated consist of a fiducial approach and bootstrap approaches, including the bias corrected and accelerated bootstrap and a bootstrap‐calibrated delta method. Based on estimated coverage probabilities, it is concluded that overall, the bootstrap‐calibrated delta method is to be preferred for computing the upper tolerance limit. Two applications are also discussed; the first application is on the analysis of data on health care expenditures, and the second application is on testing the safety of body armor.

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Confidence intervals for the mean and a percentile based on zero-inflated lognormal data

Cited by 34 publications

References 25 publications

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

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

Bayesian confidence intervals for the difference between variances of delta‐lognormal distributions

Tolerance limits under zero‐inflated lognormal and gamma distributions

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