SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS

Halil Aydoğdu

doi:10.1501/Commua1_0000000186

Year 2007, Volume: 56 Issue: 2, 17 - 25, 01.08.2007

Halil Aydoğdu

https://doi.org/10.1501/Commua1_0000000186

Abstract

References

Aydo¼gdu, H. and Öztürk, F., ”Some Monotonicity Properties of Age and Excess Lifetime in Renewal Processes”, Jour. of Inst. of Math. and Comp. Sci. (Math. Ser.) Vol.10, No.3 (1997) 145-150.
Aydo¼gdu, H., ”A Pointwise Estimator for the k-fold Convolution of a Distribution Function”, Commun. Statist. Theor. Meth. 34 (2005) 1939-1956.
Barlow, E. R. and Proschan, F., Mathematical Theory of Reliability. John Wiley & Sons, Inc., New York (1965).
Barlow, E. R. and Proschan, F., Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, Inc. New York (1981).
Bergstrom, T. and Bagnoli, M., Log-Concave Probability and Its Applications. University of California, Postprints, Paper 11 (2005). Current address : Ankara University, Faculty of Sciences, Department of Statistics, 06100
Tando¼gan-Ankara, Turkey E-mail address : aydogdu@science.ankara.edu.tr

SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS

Year 2007, Volume: 56 Issue: 2, 17 - 25, 01.08.2007

Halil Aydoğdu

https://doi.org/10.1501/Commua1_0000000186

Abstract

In general it is impossible to obtain analytical expressions for the
n-fold convolution F
n of a distribution function F. Existence of bounds for
F
n is of great value. In this study some bounds for F
n are given with the help
of the probability integral transformation when F is concave or log-concave.

Keywords

Convolution, concave df, log-concave df

References

Aydo¼gdu, H. and Öztürk, F., ”Some Monotonicity Properties of Age and Excess Lifetime in Renewal Processes”, Jour. of Inst. of Math. and Comp. Sci. (Math. Ser.) Vol.10, No.3 (1997) 145-150.
Aydo¼gdu, H., ”A Pointwise Estimator for the k-fold Convolution of a Distribution Function”, Commun. Statist. Theor. Meth. 34 (2005) 1939-1956.
Barlow, E. R. and Proschan, F., Mathematical Theory of Reliability. John Wiley & Sons, Inc., New York (1965).
Barlow, E. R. and Proschan, F., Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, Inc. New York (1981).
Bergstrom, T. and Bagnoli, M., Log-Concave Probability and Its Applications. University of California, Postprints, Paper 11 (2005). Current address : Ankara University, Faculty of Sciences, Department of Statistics, 06100
Tando¼gan-Ankara, Turkey E-mail address : aydogdu@science.ankara.edu.tr

There are 6 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Halil Aydoğdu This is me
Publication Date	August 1, 2007
Published in Issue	Year 2007 Volume: 56 Issue: 2

Cite

APA	Aydoğdu, H. (2007). SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 56(2), 17-25. https://doi.org/10.1501/Commua1_0000000186
AMA	Aydoğdu H. SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2007;56(2):17-25. doi:10.1501/Commua1_0000000186
Chicago	Aydoğdu, Halil. “SOME BOUNDS FOR THE N-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56, no. 2 (August 2007): 17-25. https://doi.org/10.1501/Commua1_0000000186.
EndNote	Aydoğdu H (August 1, 2007) SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56 2 17–25.
IEEE	H. Aydoğdu, “SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 56, no. 2, pp. 17–25, 2007, doi: 10.1501/Commua1_0000000186.
ISNAD	Aydoğdu, Halil. “SOME BOUNDS FOR THE N-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56/2 (August 2007), 17-25. https://doi.org/10.1501/Commua1_0000000186.
JAMA	Aydoğdu H. SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2007;56:17–25.
MLA	Aydoğdu, Halil. “SOME BOUNDS FOR THE N-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 56, no. 2, 2007, pp. 17-25, doi:10.1501/Commua1_0000000186.
Vancouver	Aydoğdu H. SOME BOUNDS FOR THE n-FOLD CONVOLUTION OF CONCAVE AND LOG-CONCAVE DISTRIBUTION FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2007;56(2):17-25.