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

Halil Aydoğdu

doi:10.1501/Commua1_0000000186

Year 2007, , 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, , 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

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.