Hypothesis testing for normal distributions: A unified framework and new developments

Yuejin Zhou, Sze Yui Ho, Jiahua Liu, Tiejun Tong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)
29 Downloads (Pure)


Hypothesis testing for normal distributions is one important problem in statistics and related fields including management science, engineering science and medical science. In this paper, from a very unique perspective, we propose a unified framework to comprehensively review the existing literature on the one- and two-sample testing problems of normal distributions. The unified framework has integrated the literature in a way that it includes most commonly used tests as special cases, including the one-sample mean test, the one-sample variance test, the two-sample mean test, the two-sample variance test, and the Behrens-Fisher test. The unified framework has also put forward two new hypothesis tests that are rarely studied in the literature. To complete the puzzle, we propose two likelihood ratio test statistics to solve those new testing problems. Simulation studies and real data examples are also provided to demonstrate that our proposed test statistics are appropriate for practical implementation.

Original languageEnglish
Pages (from-to)167-179
Number of pages13
JournalStatistics and its Interface
Issue number2
Publication statusPublished - 30 Jan 2020

Scopus Subject Areas

  • Statistics and Probability
  • Applied Mathematics

User-Defined Keywords

  • Hypothesis test
  • Likelihood ratio test
  • Normal distribution
  • Unified framework


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