# ON CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENT PROPERTY OF RECORD VALUES

• Lee, Min-Young (Department of Mathematics Dankook University) ;
• Lim, Eun-Hyuk (Department of Mathematics Dankook University)
• Accepted : 2010.04.23
• Published : 2010.06.30

#### Abstract

We present characterizations of the Weibull distribution by the independent property of record values that F(x) has a Weibull distribution if and only if $\frac{X_{U(m)}}{X_{U(n)}}$ and $X_{U(n)}$ or $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(n)}$ are independent for \$1{\leq}m.

#### Acknowledgement

Supported by : Dankook university

#### References

1. J. Aczel, Lectures on Functional Equations and Their Applications, Academic Press, NY, 1996.
2. M. Ahsanullah, Record Statistics, Inc, Dommack NY, 1995.
3. J. Galambos & S. Kotz , Characterization of Probability Distributions, Lecture Notes in Mathematics, 675, Springer-Verlag, NY, 1978.
4. M.Y. Lee & S.K. Chang, Characterizations of the weibull distribution by the independence of the record values, J. Appl. Math. & Computing, 15 (2008), 163-167.