Small Sample Confidence Intervals in Log Space Back-Transformed from Normal Space

Abstract

The logarithmic transformation is commonly applied to a lognormal data set to improve symmetry, homoscedasticity, and liearity. Simple to implement and easy to understand, the logarithm function transforms the original data to closely resemble a normal distribution. Analysis in the normal space provides point estimates and confidence intervals, but transformation back to the original space using the naive approach yields confidence intervals of impractical width. The naive approach offers results that are often inadequate for practical purpose. We present an alternative approach that provides improved results in the form of decreased interval width, increased confidence level, or both. Our alternative approach yields dramatically improved results at small sample sizes drawn from the right tail of the lognormal distribution.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2006
Accession Number
ADA450276

Entities

People

  • Jason E. Tisdel

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Confidence Limits
  • Data Science
  • Data Sets
  • Distribution Functions
  • Estimators
  • Information Science
  • Intervals
  • Literature Surveys
  • Logarithm Functions
  • Normal Distribution
  • Probability
  • Random Variables
  • Simulations
  • Standards
  • Statistics
  • Symmetry

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.

Technology Areas

  • Space