Some characterizations of raised cosine distribution

Authors

  • M Ahsanullah

    Professor of Statistics, Professor of Statistics, Department of Information Systems and Supply Chain Management, Rider University, Lawrenceville, NJ, USA

  • M Shakil

    Professor of Mathematics, Department of Liberal Arts and Sciences - Mathematics, Miami Dade College, Hialeah Campus, 1780 West 49th Street, Suite 2325, Hialeah, Fl. 33012, USA

Received date: July 2, 2018

Accepted date: July 14, 2018

Published date: August 10, 2018

DOI:

https://doi.org/10.14419/ijasp.v6i2.14988

Keywords:

Characterization, Raised cosine distribution, Truncated first moment.

Abstract

Some distributional properties of the raised cosine distribution are presented. Based on the distributional properties, several new characterizations of the raised cosine distribution are given.

 

Author Biography

  • M Ahsanullah, Professor of Statistics, Professor of Statistics, Department of Information Systems and Supply Chain Management, Rider University, Lawrenceville, NJ, USA
    Liberal Arts and Sciece Department (Mathematics), Professor

References

  1. [1] Ahsanullah, M. (1995). Record Statistics, Nova Science Publishers, New York, USA.

    [2] Ahsanullah, M. (2017). Characterizations of Univariate Continuous Distributions, Atlantis-Press, Paris, France.

    [3] Ahsanullah, M., Nevzorov,V. B., and Shakil, M. (2013). An Introduction to Order Statistics, Atlantis-Press, Paris, France. https://doi.org/10.2991/978-94-91216-83-1.

    [4] Ahsanullah, M., Kibria, B. M. G., and Shakil, M. (2014). Normal and Student´s t Distributions and Their Applications, Atlantis Press, Paris, France. https://doi.org/10.2991/978-94-6239-061-4.

    [5] Ahsanullah, M., Shakil, M., and Kibria, B. G. (2015). Characterizations of folded student’s t distribution. Journal of Statistical Distributions and Applications, 2(1), 15. https://doi.org/10.1186/s40488-015-0037-5.

    [6] Ahsanullah, M., Shakil, M., & Kibria, B. M. (2016). Characterizations of Continuous Distributions by Truncated Moment. Journal of Modern Applied Statistical Methods, 15(1) 17. https://doi.org/10.22237/jmasm/1462076160.

    [7] Arnold, B.C., Balakrishnan, and Nagaraja, H. N. (2005). First Course in Order Statistics, Wiley, New York, USA.

    [8] David, H. A., and Nagaraja, H. N. (2003). Order Statistics, Third Edition, Wiley, New York, USA. https://doi.org/10.1002/0471722162.

    [9] Galambos, J., and Kotz, S. (1978). Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models, Lecture Notes in Mathematics, 675, Springer, Berlin.

    [10] Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75 – 84. https://doi.org/10.1007/978-94-009-3965-3_8.

    [11] Glänzel, W., Telcs, A., and Schubert, A. Characterization by truncated moments and its application to Pearson-type distributions. Z. Wahrsch. Verw. Gebiete, 66,

    [12] Gradshteyn, I. S., and Ryzhik, I. M. (1990). Table of integrals, series, and products, Academic Press, Inc., San Diego, California, USA.

    [13] King, M. (2017). Statistics for Process Control Engineers: A Practical Approach, First Edition, Wiley, New York, USA. https://doi.org/10.1002/9781119383536.

    [14] Kotz, S., and Shanbhag, D. N. (1980). Some new approaches to probability distributions. Advances in Applied Probability, 12, 903 - 921. https://doi.org/10.2307/1426748.

    [15] Kyurkchiev, V., and Kyurkchiev, N. (2016). On the approximation of the step function by raised-cosine and laplace cumulative distribution functions. European International Journal of Science and Technology, 4(9), 75 - 84.

    [16] Mathai, A. M. and Saxena, R. K. (1973). Generalized Hypergeometric Functions with ApplicationsIn Statistics and Physical Sciences, Lecture Notes No. 348. Springer-Verlag, Heidelberg, Germany.

    [17] Nagaraja, H. (2006). Characterizations of Probability Distributions. In Springer Handbook of Engineering Statistics (pp. 79 - 95), Springer, London, UK. https://doi.org/10.1007/978-1-84628-288-1_4.

    [18] Nevzorov, V. B. (2001). Records: Mathematical Theory, Translation of Mathematical Monograph. American Mathematical Society, Rhode Island, USA.

    [19] Prudnkov, A. P., Brychkov, Yu. A., and Marichev, O. I. (1986). Integrals and Series, Vol. 1, Gordon and Breach, New York, USA.

    [20] Prudnkov, A. P., Brychkov, Yu. A., and Marichev, O. I. (1989). Integrals and Series, Vol. 3: More Special Functions, Gordon and Breach, New York, USA.

    [21] Rinne, H. (2010). Location–Scale Distribution: Linear Estimation and Probability Plotting Using MATLAB, Copyright: Prof. em. Dr Hors Rinne, Department of Economics and Management Science, Justus–Lieblig–University, Giessen, Germany.

    [22] Slater, L. J. (1966). Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, England, UK.

    [23] Willink, R. (2013). Measurement Uncertainty and Probability, Cambridge University Press, First Edition, New York, USA. https://doi.org/10.1017/CBO9781139135085.

Downloads

Additional Files

Received date: July 2, 2018

Accepted date: July 14, 2018

Published date: August 10, 2018