Main Article Content
The present paper intends to revisit the distribution of the ratio of the range to the sample standard deviation, known as the distribution of the internally studentized range, in the normal case. This distribution has its importance recognized in several areas, as quality control and inference, for testing the lack of homogeneity of the data or kurtosis. An alternative distribution to the one presented by David et al. (1954), based on the distribution of the maximum, is proposed. We exhibit a detailed proof for the distribution of the internally studentized range in the normal case and sample size 3. We also provide a new result: the distribution for the uniform case with sample of size 3.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).