Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions

Weizhong Tian (), Yaoting Yang and Tingting Tong
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Weizhong Tian: College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China
Yaoting Yang: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China
Tingting Tong: Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA

Mathematics, 2022, vol. 10, issue 16, 1-14

Abstract: In this paper, we study the inferences of the difference of medians for two independent log-normal distributions. These methods include traditional methods such as the parametric bootstrap approach, the normal approximation approach, the method of variance estimates recovery approach, and the generalized confidence interval approach. The simultaneous confidence intervals for the difference in the median for more than two independent log-normal distributions are also discussed. Our simulation studies evaluate the performances of the proposed confidence intervals in terms of coverage probabilities and average lengths. We find that the parametric bootstrap approach would be a suitable choice for smaller sample sizes for the two independent distributions and multiple independent distributions. However, the method of variance estimates recovery and normal approximation approaches are alternative competitors for constructing simultaneous confidence intervals, especially when the populations have large variance. We also include two practical applications demonstrating the use of the techniques on observed data, where one data set works for the PM2.5 mass concentrations in Bangkapi and Dindaeng in Thailand and the other data came from the study of nitrogen-bound bovine serum albumin produced by three groups of diabetic mice. Both applications show that the confidence intervals from the parametric bootstrap approach have the smallest length.

Keywords: log-normal distribution; fiducial generalized confidence interval; normal approximation; method of variance estimates recovery (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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