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

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  • Wei-Hwa Wu
  • Hsin-Neng Hsieh

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.

Suggested Citation

  • Wei-Hwa Wu & Hsin-Neng Hsieh, 2014. "Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1471-1485, July.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:7:p:1471-1485
    DOI: 10.1080/02664763.2014.881780
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    Cited by:

    1. Hsin-Neng Hsieh & Hung-Yi Lu, 2020. "The generalized inference on the ratio of mean differences for fraction retention noninferiority hypothesis," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-12, June.
    2. Philip L.H. Yu & Thomas Mathew & Yuanyuan Zhu, 2017. "A generalized pivotal quantity approach to portfolio selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1402-1420, June.

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