Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Inequalities for Some Multivariate f-Distributions with Applications

John E. Hewett and William G. Bulgren
Technometrics
Vol. 13, No. 2 (May, 1971), pp. 397-402
DOI: 10.2307/1266800
Stable URL: http://www.jstor.org/stable/1266800
Page Count: 6
  • Download ($14.00)
  • Cite this Item
Inequalities for Some Multivariate f-Distributions with Applications
Preview not available

Abstract

The inequality Pr(a≤ Wi≤ b;i=1,2,⋯ ,n)≥ Π i=1 n Pr(a≤ Wi≤ b) is shown to hold when the random variables W1,⋯ ,Wn have a particular multivariate f-distribution which is defined. It is used in this paper to construct conservative simultaneous prediction intervals for failure times in certain life test experiments. An additional inequality is shown to hold for all bivariate distributions belonging to a class of bivariate f-distributions which is defined. An indication of the use of this latter inequality is given. Some tables are included which indicate the sharpness of each of the inequalities.

Page Thumbnails

  • Thumbnail: Page 
397
    397
  • Thumbnail: Page 
398
    398
  • Thumbnail: Page 
399
    399
  • Thumbnail: Page 
400
    400
  • Thumbnail: Page 
401
    401
  • Thumbnail: Page 
402
    402