Regularized t distribution: definition, properties and applications

Zongliang Hu, Yiping Yang*, Gaorong Li, Tiejun Tong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


For gene expression data analysis, an important task is to identify genes that are differentially expressed between two or more groups. Nevertheless, as biological experiments are often measured with a relatively small number of samples, how to accurately estimate the variances of gene expression becomes a challenging issue. To tackle this problem, we introduce a regularized t distribution and derive its statistical properties including the probability density function and the moment generating function. The noncentral regularized t distribution is also introduced for computing the statistical power of hypothesis testing. For practical applications, we apply the regularized t distribution to establish the null distribution of the regularized t statistic, and then formulate it as a regularized t-test for detecting the differentially expressed genes. Simulation studies and real data analysis show that our regularized t-test performs much better than the Bayesian t-test in the “limma” package, in particular when the sample sizes are small.
Original languageEnglish
Pages (from-to)1884-1900
Number of pages17
JournalScandinavian Journal of Statistics
Issue number4
Early online date14 Apr 2023
Publication statusPublished - Dec 2023

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Bayesian t-test
  • hypothesis testing
  • noncentral regularized t distribution
  • regularized t distribution
  • regularized t-test


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