On the Discrimination Between Two Location and Scale Parameter Models

Srinivasan, R.; Antle, C. E.

doi:10.1007/978-94-010-1845-6_6

R. Srinivasan^4,5 &
C. E. Antle^4,5

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 17))

266 Accesses
1 Citations

Abstract

Let x_i1, x_i2,…, x_in, for i=1, 2,…, k, denote independent ran- dome samples of size n each from k distinct populations, the probability density function (pdf) corresponding to the ith population being (l/b_i)f[(x-a_i)/bi], -∞ < a_i < ∞, b_i > 0, where f(x) is a prototype pdf which defines the family of distributions common to the k populations. Let it further be assumed that the location and scale parameters, a_i, b_i, are unknown and are possibly different for the different populations. Suppose that we are able to assume that f is either one of the two specified families of pdf, f1 and f2. The problem of discrimination reviewed here is that of finding a decision rule which selects one of these two families as the true pdf.

Research supported in part by Aerospace Research Laboratories, Air Force Systems Command, United States Air Force, Contract No. FY 8994-73-00040/0771.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 169.00; Price excludes VAT (USA)

Softcover Book: USD 249.99; Price excludes VAT (USA)

Hardcover Book: USD 219.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Aivazyan, S.A. (1959). Theory of Prob. and its Applns., 4, 83–9.
Article Google Scholar
Antle, C.E. (1972). Choice of model for reliability studies and related topics, Aerospace Research Laboratories Report, United States Air Force, Wright Patterson Air Force Base, Ohio.
Google Scholar
Antle, C.E. & Bain, L.J. (1969). SIAM Review, 11, 251–3.
Article MathSciNet MATH Google Scholar
Antle, C.E. & Klimko, L.A. (1973). Choice of model and related topics II, Aerospace Research Laboratories Report, United States Air Force, Wright Patterson Air Force Base, Ohio.
Google Scholar
Arley, N. (1940). Mat. Pys. Medd. Danske Vid. Selsk., 18, 3.
MathSciNet Google Scholar
Bol’shev, L.N. (1959). Theory of Prob. and its Applns., 4, 129–41.
Article MATH Google Scholar
Bol’shev, L.N. (1965). Theory of Prob. and its Applns., 10, 694–6.
Google Scholar
Bondesson, L. (1974). Personal Communication, to appear in Z. Wahrscneinlichkeitstheorie.
Google Scholar
Cox, D.R. (1961). Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, Berkeley, University of California Press, 105–23.
Google Scholar
Cox, D.R. (1962). Journal of the Royal Statistical Society, series B, 24, 406–24.
Google Scholar
David, H.A., Hartley, H.O. & Pearson, E.S. (1954). Biometrika, 41, 482–93.
MathSciNet MATH Google Scholar
Dumonceaux, R. & Antle, C.E. (1973). Technometrics, 15, 923–6.
Article MathSciNet MATH Google Scholar
Dumonceaux, R., Antle, C.E. & Haas, C. (1973). Technometrics, 15, 19–27.
Article MathSciNet MATH Google Scholar
Dyer, A.R. (1971), Technical Memorandum No. 18, Aberdeen Research and Development Center, Aberdeen Proving Ground, Maryland.
Google Scholar
Grubbs, F.E. (1950). Annals of Mathematical Statistics, 21, 27–58.
Article MathSciNet MATH Google Scholar
Hajek, J. & Sidak, S. (1967). Theory of Rank Tests, Academic Press, New York.
MATH Google Scholar
Hogg, R.V., Uthoff, V.A., Randies, R.H. & Davenport, A.S. (1972). Journal of the American Statistical Association, 67, 597–600.
Article MathSciNet MATH Google Scholar
Jackson, O.A.Y. (1968). Biometrika, 55, 355–63.
Article MathSciNet Google Scholar
Jackson, O.A.Y. (1969). Applied Statistics, 18, 70–5.
Article Google Scholar
Kanofsky, P., Kotz, S. & Srinivasan, R. (1970). Statistical Analysis of Physiological Variation, NIH Technical Report.
Google Scholar
Khakhubiya, R.G. (1966). Theory of Prob. and its Applns.,.1, 166–72.
Google Scholar
Kotz, S. (1973). Communications in Statistics, 1, 113–32.
Article MathSciNet Google Scholar
Lehmann, E.L. (1959). Testing Statistical Hypotheses. Wiley, New York.
MATH Google Scholar
Pearson, E.S. (1936). Biometrika, 28, 308–20.
MATH Google Scholar
Pearson, E.S. & Stephens, M.A. (1964). Biometrika, 51, 484–7.
MathSciNet MATH Google Scholar
Petrov, A. A. (1951). Kokl, Akad, Nauk SSSR., 76, 355–8.
MATH Google Scholar
Petrov, A.A. (1956). Theory of Prob. and its Applns., 1, 223–45.
Article Google Scholar
Prokhorov, Yu.V. (1965). Theory of Prob. and its Applns., 10, 438–45.
Article Google Scholar
Roy, A.D. (1950). Economic Journal, 60, 831–36.
Article Google Scholar
Smirnov, N. V. (1941). Kokl, Akad, Nauk SSSR., 33, 346–9.
Google Scholar
Stacy, E.W. (1962). Annals of Mathematical Statistics, 33, 1187–92.
Article MathSciNet MATH Google Scholar
Uthoff, V.A. (1970). Journal of the American Statistical Association, 65, 1597–1600.
Article MathSciNet MATH Google Scholar
Uthoff, V.A. (1973). Annals of Mathematical Statistics, 19 170–4.
MathSciNet Google Scholar
Volodin, I.N. (1965). Theory of Prob. and its Applns., 10, 335–8.
Article MathSciNet MATH Google Scholar
Volodin, I.N. (1966). Probability Methods and Cybernitics, 4, Uch. Zap. Kazan. G. U. 125, 6, 3–23. (In Russian)
Google Scholar
Volodin, I.N. (1967). Theory of Prob. and its Applns., 12, 519–25.
Article MathSciNet MATH Google Scholar
Volodin, I.N. (1969). Theory of Prob. and its Applns., 14, 320–4.
Article MathSciNet Google Scholar
Volodin, I.N. (1973). Selected Translations in Mathematical Statistics and Probability, 11, 1–26.
Google Scholar
Volodin, I.N. (1974). Theory of Prob. and its Applns., 19, 398–404. (In Russian)
Google Scholar
Wald, A. (1947). Sequential Analysis. Wiley, New York.
MATH Google Scholar
Walker, A.M. (1967). Biometrika, 54, 38–68.
Google Scholar
Yalovsky, M. (1974). Personal Communication.
Google Scholar

Download references

Author information

Authors and Affiliations

Temple University, USA
R. Srinivasan & C. E. Antle
Pennsylvania State University, USA
R. Srinivasan & C. E. Antle

Authors

R. Srinivasan
View author publications
You can also search for this author in PubMed Google Scholar
C. E. Antle
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

The Pennsylvania State University, University Park, Pa., USA
G. P. Patil
Temple University, Philadelphia, Pa., USA
S. Kotz
University of Warwick, Coventry, England
J. K. Ord

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Srinivasan, R., Antle, C.E. (1975). On the Discrimination Between Two Location and Scale Parameter Models. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1845-6_6

Download citation

DOI: https://doi.org/10.1007/978-94-010-1845-6_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1847-0
Online ISBN: 978-94-010-1845-6
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics