On using Shannon entropy measure for formulating new weighted exponential distribution

References

• Fisher RA. The effects of methods of ascertainment upon the estimation of frequencies. Ann Eugen. 1934;6(1):13–25.
   Google Scholar
• Rao CR. On discrete distributions arising out of methods of ascertainment. In: Patil GP, editor. Classical and contagious discrete distribution. Calcutta: Pergamon Press and Statistical Publishing Society; 1965, 27(2); p. 311–324.
   Google Scholar
• Cox DR. Some sampling problems in technology. In: Johnson NL, Smith H, editor. New developments in survey sampling. New York: John Wiley and Sons; 1968. p. 506–527.
   Google Scholar
• Al-Nasser AD, Al-Omari A, Ciavolino E. A size-biased Ishita distribution and application to real data. Qual Quant. 2019;53(1):493–512.
   Google Scholar
• Shannon CE. A mathematical theory of communication. Reprinted with Corrections from the Bell Syst Tech J. 1948;27(3):379–423.
   Google Scholar
• Rezzoky A, Nadhel Z. Mathematical study of weighted generalized exponential distribution. Journal of the College of Basic Education. 2015;21(89):165–172.
   Google Scholar
• Mir K, Ahmed A, Reshi J. Structural properties of length biased Beta distribution of first kind. American Journal of Engineering Research. 2013;2:01–06.
   Google Scholar
• Mudasir S, Ahmad S. Structural properties of length-biased Nakagami distribution. International Journal of Modern Mathematical Sciences. 2015;13(3):217–227.
   Google Scholar
• Shi X, Broderick O, Pararai M. Theoretical properties of weighted generalized Rayleigh and related distributions. Theoretical Mathematics and Applications. 2012;2:45–62.
   Google Scholar
• Ye Y, Oluyede B, Pararai M. Weighted generalized Beta distribution of the second kind and related distributions. Journal of Statistical and Econometric Methods. 2012;1:13–31.
   Google Scholar
• Das K, Roy T. Applicability of length biased generalized Rayleigh distribution. Advances in Applied Science Research. 2011;2:320–327.
   Google Scholar
• Jabeen S, Jan T. Information measures of size biased generalized Gamma distribution. International Journal of Scientific Engineering and Applied Science. 2015;1:2395–3470.
   Google Scholar
• Aleem M, Sufyan M, Khan N. A Class of Modified weighted Weibull distribution and its properties. American Review of Mathematics and Statistics. 2013;1:29–37.
   Google Scholar
• Castillo J, Casany M. Weighted Poisson distribution for over dispersion and under dispersion solutions. Annals of Institute of Statistical Mathematics. 1998;50:567–585.
   Web of Science ®Google Scholar
• Larose D, Dey D. Weighted distributions viewed in the context of model selection: A bayesian perspective. Test. 1996;5(1):227–246.
   Google Scholar
• Mahfoud M, Patil G. On weighted distributions. In: Kallianpur G. et al. editors. Statistics and probability essays in honor of C. R. Rao. Amsterdam: North-Holland Publishing Company. 1982; p. 479–492.
   Google Scholar
• Al-Kadim A, Hussein A. New proposed length biased weighted exponential and rayleigh distributions with application. Mathematical Theory and Modeling. 2014;4(7):137–52.
   Google Scholar
• Al-Kadim K, Hantoosh A. Double weighted distribution and double weighted exponential distribution. Mathematical Theory and Modeling. 2013;3(5):124–34.
   Google Scholar
• Bashir S, Rasul M. Some properties of the weighted Lindley distribution. International Journal of Economics and Business Review. 2015;3:11–17.
   Google Scholar
• Modi K. Length-biased weighted Maxwell distribution. Pakistan Journal of Statistics and Operation Research. 2015;11:465–472.
   Google Scholar
• Kharazmi O, Mahdavi A, Fathizadeh M. Generalized weighted exponential distribution. Communications in Statistics – Simulation and Computation. 2014;44(6):1557–1569.
   Web of Science ®Google Scholar
• Renyi A. On measures of entropy and information. In: Jerzy Neyman editor. Proceedings of the 4th Berkeley symposium on mathematical statistic and probability. Vol. I. Contributions to Probability and Theory. Berkeley: University of California Press; 1961. p. 547–561.
   Google Scholar
• George D, George S. Marshall–Olkin Esscher transformed Laplace distribution and processes. Braz J Prob Stat. 2013;27(2):162–184.
   Web of Science ®Google Scholar
• Lindley DV. Fiducial distributions and Bayes’ Theorem. J R Stat Soc. 1958;20:102–107.
   Google Scholar
• Maydeu A, Garci A, Forero C. Goodness-of-Fit testing. International Encyclopedia of Education. 2010;7:190–196.
   Google Scholar
• Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6(2):461–464.
   Web of Science ®Google Scholar
• Akaike H. A New look at the statistical model identification. IEEE Trans Autom Control. 1974;19(6):716–723.
   Web of Science ®Google Scholar
• Bozdogan H. Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika. 1987;52(3):345–370.
   Web of Science ®Google Scholar
• Hannan EJ, Quinn BG. The determination of the order of an autoregression. J R Stat Soc B Methodol. 1979;41(2):190–195.
   Google Scholar
• Heggland K, Lindqvist BH. A nonparametric monotone maximum likelihood estimator of time trend for repairable systems data. Reliab Eng Syst Saf. 2007;92:575–584.
   Web of Science ®Google Scholar
• Stephens MA. EDF statistics for goodness of Fit and some comparisons. J Am Stat Assoc. 1974;69:730–737.
   Web of Science ®Google Scholar
• Cramér H. On the composition of elementary errors. Scand Actuar J. 1928;1928(1):13–74.
   Google Scholar
• Laha C, Laha RG. Handbook of methods of applied statistics. New York: John Wiley and Sons; 1967. 1; p. 392–394.
   Google Scholar
• Murthy DNP, Min X, Jiang R. Weibull models. New York: John Wiley and Sons; 2004. 1047(22).
   Google Scholar
• Blischke WR, Prabhakar Murthy DN. Reliability: modeling, prediction, and optimization. New York: John Wiley and Sons; 2011.
   Google Scholar