Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data

Abstract

Highly skewed and non-negative data can often be modeled by the delta-lognormal distribution in fisheries research. However, the coverage probabilities of extant interval estimation procedures are less satisfactory in small sample sizes and highly skewed data. We propose a heuristic method of estimating confidence intervals for the mean of the delta-lognormal distribution. This heuristic method is an estimation based on asymptotic generalized pivotal quantity to construct generalized confidence interval for the mean of the delta-lognormal distribution. Simulation results show that the proposed interval estimation procedure yields satisfactory coverage probabilities, expected interval lengths and reasonable relative biases. Finally, the proposed method is employed in red cod densities data for a demonstration.

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

“…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.…”

“…On the ideas of GCI, the generalized pivotal quantity (GPQ) is necessary to satisfy the two requirements of Weerahandi (1993). The GPQ of δ i based on VST was proposed by Wu & Hsieh (2014) as…”

“…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).…”

“…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).…”

Peer Review #1 of "A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand (v0.1)"

“…Aitchison and 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 and DeRouen, 1980;Hasan and Krishnamoorthy, 2018), fishery surveys (Pennington, 1983;Smith, 1988Smith, , 1990Lo et al, 1992;Fletcher, 2008;Wu and Hsieh, 2014) and medicine Tu, 1999, 2000;Tian and Wu, 2006;Hasan and Krishnamoorthy, 2018).…”