Squares of Non-Standard-Normal or Non-Student’s-t1 RVs Which Have Chi-Square1 or F1,1 Distributions: A Return Visit

Nitis Mukhopadhyay ()
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Nitis Mukhopadhyay: University of Connecticut

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 817-822

Abstract: Abstract In some quarters, especially beginners learning statistics and probability, one generally accepts a claim such as a χ 1 2 ${\chi _{1}^{2}}$ random variable (rv) must be the square of a standard normal rv or a F 1,1 rv must be the square of a Student’s t 1 rv. This feeds into more misconceptions later. Hence, we begin with a brief but general construct and then illustrate a number of rvs explicitly which are drastically different from a standard normal or Student’s t 1 rv whose squares are distributed as χ 1 2 $\chi _{1}^{2}$ or F 1,1 respectively. This simply presented note reinforces basic understanding of lessons in such core topics covered in classrooms for both undergraduate and graduate students.

Keywords: Asymmetric distributions; Cauchy distribution; Laplace distribution; Skewed distributions; Spiky distributions; Wavy distributions; Weibull distribution; 62E15; 60E05; 62H10 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-014-9425-4

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