Starlike and convex type probability distribution

  • Saurabh PorwalEmail author


The purpose of the present paper is to investigate Starlike and Convex type discrete probability distribution and obtain some results regarding moments, factorial moments, mean, variance and moment generating function for these distributions.


Probability distribution Starlike and convex functions 

Mathematics Subject Classification

97K50 30C45 



The author is thankful to the referee for his/her valuable comments and observations which helped in improving the paper.


  1. 1.
    Ahmad, M.S., Mehmood, Q., Nazeer, W., Haq, A.U.: An application of a hypergeometric distribution series on certain analytic functions. Sci. Int. (Lahore) 27(4), 2989–2992 (2015)Google Scholar
  2. 2.
    Altınkaya, S., Yalçın, S.: Poisson distribution series for analytic univalent functions. Complex Anal. Oper. Theory 12(5), 1315–1319 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bajpai, D..: A study of univalent functions associated with distribution series and \(q\)-calculus. M.Phil. Dissertation, CSJM University, Kanpur, India (2016)Google Scholar
  4. 4.
    Duren, P.L.: Univalent Functions, Grundleherem der Mathematischen Wissenchaften 259. Springer, New York (1983)Google Scholar
  5. 5.
    Gupta, S.C., Kapoor, V.K.: Fundamental of Mathematical Statistics. Sultan Chand and Sons, New Delhi (2006)Google Scholar
  6. 6.
    Murugusundaramoorthy, G., Vijaya, K., Porwal, S.: Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series. Hacet. J. Math. Stat. 45(4), 1101–1107 (2016)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Nazeer, W., Mehmood, Q., Kang, S.M., Haq, A.U.: An application of Binomial distribution series on certain analytic functions. J. Comput. Anal. Appl. 26, 11–17 (2019)MathSciNetGoogle Scholar
  8. 8.
    Porwal, S.: An application of a Poisson distribution series on certain analytic functions. J. Complex Anal. 2014, 1–3 (2014). (Art. ID 984135)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Porwal, S.: An application of certain convolution operator involving Poisson distribution series. Asian Eur. J. Math. 9(4), 8 (2016). (1650085)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Porwal, S.: Generalized distribution and its geometric properties associated with univalent functions. J. Complex Anal., 1–5 (2018) (Art. ID 8654506)Google Scholar
  11. 11.
    Porwal, S., Ahmad, D: An application of hypergeometric distribution type series on certain analytic functions. Thai. J. Math. (2019) (Art. in Press)Google Scholar
  12. 12.
    Porwal, S., Kumar, M.: A unified study on starlike and convex functions associated with Poisson distribution series. Afr. Mat. 27(5–6), 1021–1027 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Porwal, S., Kumar, S.: Confluent hypergeometric distribution and its applications on certain classes of univalent functions. Afr. Mat. 28, 1–8 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Robertson, M.S.: On the theory of univalent functions. Ann. Math. 37, 374–408 (1936)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Silverman, H.: Univalent functions with negative coefficients. Proc. Am. Math. Soc. 51, 109–116 (1975)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Lecturer MathematicsSri Radhey Lal Arya Inter CollegeHathrasIndia

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