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
    2018-08-10
    https://doi.org/10.14419/ijasp.v6i2.14988
  • 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.

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    Additional Files

  • Received date: 2018-07-02

    Accepted date: 2018-07-14

    Published date: 2018-08-10