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Inequalities for Some Multivariate f-Distributions with Applications
John E. Hewett and William G. Bulgren
Vol. 13, No. 2 (May, 1971), pp. 397-402
Published by: Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality
Stable URL: http://www.jstor.org/stable/1266800
Page Count: 6
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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.
Technometrics © 1971 American Statistical Association