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Updated fiducial distribution of parameters in the associated delta-lognormal population

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  • Yufan Wang
  • Xingzhong Xu

Abstract

In this paper we consider a special kind of semicontinous distribution. We try to concern with the situation where the probability of zero observation is associated with the location and scale parameters in lognormal distribution. We first propose a goodness-of-fit test to ensure that the data can be fit by the associated delta-lognormal distribution. Then we define the updated fiducial distributions of the parameters and establish the results that the confidence interval has asymtotically correct level while the significance level of the hypothesis testing is also asymtotically correct. We propose an exact sampling method to sample from the updated fiducial distribution. It can be seen in our simulation study that the inference on the parameters is largely improved. A real data example is also used to illustrate our method.

Suggested Citation

  • Yufan Wang & Xingzhong Xu, 2024. "Updated fiducial distribution of parameters in the associated delta-lognormal population," PLOS ONE, Public Library of Science, vol. 19(6), pages 1-19, June.
    • Handle: RePEc:plo:pone00:0298307
    DOI: 10.1371/journal.pone.0298307
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    References listed on IDEAS

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    1. Zhou Xiao-Hua & Wanzhu Tu, 1999. "Comparison of Several Independent Population Means When Their Samples Contain Log-Normal and Possibly Zero Observations," Biometrics, The International Biometric Society, vol. 55(2), pages 645-651, June.
    2. Xiao-Hua Zhou & Wanzhu Tu, 2000. "Confidence Intervals for the Mean of Diagnostic Test Charge Data Containing Zeros," Biometrics, The International Biometric Society, vol. 56(4), pages 1118-1125, December.
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