Pacific Journal of Mathematics

Minimizing integrals in certain classes of monotone functions.

H. D. Brunk, G. M. Ewing, and W. R. Utz

Article information

Source
Pacific J. Math., Volume 7, Number 1 (1957), 833-847.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103043663

Mathematical Reviews number (MathSciNet)
MR0087025

Zentralblatt MATH identifier
0080.34101

Subjects
Primary: 49.0X

Citation

Brunk, H. D.; Ewing, G. M.; Utz, W. R. Minimizing integrals in certain classes of monotone functions. Pacific J. Math. 7 (1957), no. 1, 833--847. https://projecteuclid.org/euclid.pjm/1103043663


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References

  • [1] Miriam Ayer, H. D. Brunk, G. M. Ewing, W. T. Reid and Edward Silverman, An empirical distribution function for sampling with incomplete information,Ann. Math. Stat. 26 (1955), 41-47.
  • [2] H. D. Brunk, G. M. Ewing and W. T. Reid, The minimum of a certain definite integral suggested by the maximumlikelihood estimate of a distribution function, Bull. Amer. Math. Soc, 60 (1954), 535.
  • [3] H. D. Brunk, Maximumlikelihood estimates of monotone parameters,Ann. Math. Stat. 26 (1955), 607-16.
  • [4] H. D. Brunk, G. M. Ewing and W. R. Utz, Some Helly Theorems for monotone functions, Proc. Amer. Math. Soc. 7 (1956), 776-83.
  • [5] H. Cramer, Mathematicalmethods of statistics, Princeton University Press, 1946.
  • [6] P. R. Halmos, Measure theory, Van Nostrand, New York, 1950.
  • [7] E. J. McShane, Integration, Princeton University Press, 1944.
  • [8] M. E. Munroe, Introductionto measure theory and integration,Addison-Wesley, Cambridge, Mass., 1953.