Characterization of Family of Rayleigh Distribution Through Record Values

Main Article Content

M. I. Khan, Abdelfattah Mustafa


An observation that shows greater than all the preceding observations, is called record. The characterization results via conditional expectation based on record values are expressed for family of Rayleigh distribution. Moreover, entropies based on distribution function are discussed and enumerated.

Article Details


  1. K.N. Chandler, The Distribution and Frequency of Record Values, J. R. Stat. Soc. Ser. B: Stat. Methodol. 14 (1952), 220–228.
  2. M. Ahsanullah, Record Statistics, Nova Sciences Publishers, New York, 1995.
  3. B.C. Arnold, N. Balakrshinan, H.N. Nagaraja, Records, Wiley, New York, 1998.
  4. V.B. Nevzorov, Records: Mathematical Theory, American Mathematical Society, Providence, Rhode Island, 2000.
  5. N.M. Kilany, M.A.W. Mahmoud and L. H. El-Refai, Power Rayleigh Distribution for Fitting Total Deaths of COVID19 in Egypt, J. Stat. Appl. Prob. 12 (2023), 1073–1085.
  6. J.M.A. Nashaat, Estimation of Two Parameter Powered Inverse Rayleigh Distribution, Pak. J. Stat. 36 (2020), 117–133.
  7. I. Malinowska, D. Szynal, On Characterization of Certain Distributions of k th Lower (Upper) Record Values, Appl. Math. Comput. 202 (2008), 338–347.
  8. A.I. Shawky, R.A. Bakoban, Conditional Expectation of Certain Distributions of Record Values, Int. J. Math. Anal. 3 (2009), 829–838.
  9. M. Faizan, M.I. Khan, A Characterization of Continuous Distributions Through Lower Record Statistics, ProbStat Forum, 4 (2011), 39–43.
  10. D. Kumar and M.I. Khan, Recurrence Relations for Moments of k Record Values From Generalized Beta II Distribution and a Characterization, Selcuk J. Appl. Math. 13 (2012), 75–82.
  11. S. Minimol, P.Y. Thomas, On Some Properties of Makeham Distribution Using Generalized Record Values and Its Characterization, Brazil. J. Prob. Stat. 27 (2013), 487–501.
  12. M.A. Selim, H.M. Salem, Recurrence Relations for Moments of k-th Upper Record Values from Flexible Weibull Distribution and a Characterization, Amer. J. Appl. Math. Stat. 2 (2014), 168–171.
  13. M.I. Khan, Characterization of General Class of Distribution Based on Upper Record Values, Int. J. Agric. Stat. Sci. 11 (2015), 43–45.
  14. M.I. Khan, M.A.R. Khan, Generalized Record Values from Distributions Having Power Hazard Function and Characterization, J. Stat. Appl. Prob. 8 (2019), 103–111.
  15. M.I. Khan, Note on Characterization of Linear Hazard Rate Distribution by Generalized Record Values, Appl. Math. E-Notes, 20 (2020), 398–405.
  16. M.I. Khan, Characterization of a New Family of Distribution Through Upper Record Values, Tamkang J. Math. 52 (2021), 309–316.
  17. M.I. Khan, Power-Linear Hazard Distribution via k-th Record Values and Characterization, Appl. Math. Inf. Sci. 17 (2023), 735–739.
  18. C.E. Shannon, A Mathematical Theory of Communication, Bell Syst. Techn. J. 27 (1948), 379–423.
  19. M. Rao, Y. Chen, B.C. Vemuri, F. Wang, Cumulative Residual Entropy: A New Measure of Information, IEEE Trans. Inf. Theory. 50 (2004), 1220–1228.
  20. A. Di Crescenzo, M. Longobardi, On Cumulative Entropies, J. Stat. Plan. Inference. 139 (2009), 4072–4087.