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2020 | 145 | 16-30
Article title

Extended Lognormal Distribution: Properties and Applications

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This paper is devoted to study a form of lognormal distributions family and introduce some of its basic properties. It presents new derivate models that find many applications will be useful for practitioners in various fields. The abstract explores some of the basic characteristics of the family of abnormal distributions and provides some practical methods for analyzing some different applied fields related to theoretical and applied statistical sciences. The proposed model allows for the improvement of the relevance of near-real data and opens broad horizons for the study of phenomena that can be addressed through the results obtained. This study is devoted to a review of fitting data, discuss distribution laws for models and describe the approaches used for parameterization and classification of models. Finally, a set of concluding observations has been developed to track the mix distributions and their adaptation mechanisms.
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  • Department of Basic Sciences Prep. Year, P.O. Box 2440, University of Hail, Hail, Kingdom of Saudi Arabia
  • [1] Aitchison, J. and Brown, J.A.C, (1963). The Lognormal Distribution. Cambridge at the University Press.
  • [2] Alexander Katz, Jimin Khim and Christopher Williams., (2018). Log-normal Distribution. web site (09/02/2018):
  • [3] Al-Hussaini. E.K., Mousa. M.A., and Sultan. K.S., (1997). Parametric and Nonparametric Estimation of F(X<x) for Finite Mixtures of Lognormal Components. Communications in Statistics. Theory and Methods, Vol. 26, No.5, pp 1269-1289
  • [4] Bachioua, Lahcene (2018). On Recent Modifications of Extended Weibull Families Distributions and Its Applications. Asian Journal of Fuzzy and Applied Mathematics, Vol. 6, No. 1, pp. 1-12.
  • [5] Bachioua Lahcene (2018). On Recent Modifications of Extended Rayleigh Distribution and its Applications. JP Journal of Fundamental and Applied Statistics, Vol. 12, Issue 1: pp. 1-13.
  • [6] Bachioua Lahcene, (2019). On Extended Normal Inverse Gaussian Distribution: Theory, Methodology, Properties and Applications. American Journal of Applied Mathematics and Statistics, Vol. 7, No 6. 224-230
  • [7] Edwin L. Crow and Kunio Shimizu, (1988). Lognormal Distributions: Theory and Applications. Statistics: A Series of Textbooks and Monographs, Vol. 88, edition (CRC Press).
  • [8] Eeckhout, J., (2004). Gibrat’s Law For (All) Cities. American Economic Review, Vol. 94, No. 5, pp. 1429-1451.
  • [9] Eeckhout, J., (2009)."Gibrat’s Law for (All) Cities: Reply. American Economic Review, Vol. 99, No. 4, pp 1676-1683
  • [10] Gabaix, X., (1999a). Zipf’s Law and the Growth of Cities. American Economic Review Vol. 89, No. 2, pp 129-132
  • [11] Gabaix, X., (1999b). Zipf’s Law For Cities: an Explanation. The Quarterly Journal of Economics, 114(3), 739-767.
  • [12] Goodwin, B. K., and A. P. Ker., (2002). Modeling Price and Yield Risk, A Comprehensive Assessment of the Role of Risk in US Agriculture Just, R. and R. Pope, ed. Norwell Maryland: Kluwer, pp 289-323.
  • [13] Hobson, E. W V., Sc.D., LL.D., F.R.S., (1914). John Napier and the Invention of Logarithms, Cambridge: at the University Press.
  • [14] Hribar Lovre (2008). Usage of Weibull and other Models for Software Faults Prediction in AXE",
  • [15] Jung, A. R., and C.A. Ramezani (1999).Valuing Risk Management Tools as Complex Derivatives: An Application to Revenue Insurance. Journal of Financial Engineering No. 8: pp 99-120.
  • [16] Kececioglu, Dimitri (1991). Reliability Engineering Handbook, Vol. 1, Prentice Hall, Inc., Englewood Cliffs, New Jersey.
  • [17] Leipnik, R.B., (1991)."On Lognormal Random Variables: The Characteristic Function. J. Australian Math. Soc. Ser. B Vol. 32: pp 327-347.
  • [18] Limpert, E., Stahel, W.A., and Abbt, M., (2001). Lognormal Distributions Across the Sciences: Keys and Clues. Bioscience No. 51: pp 341-352.
  • [19] Marlow, N.A., (1967). A Normal Limit Theorem for Power Sums of Independent Random Variables. Bell System Technical J. Vol. 46: pp 2081-2089.
  • [20] Mitchell, R.L. (1968). Permanence of the Lognormal Distribution. J. Optical Society of America, Vol. 58: pp 1267-1272
  • [21] Stokes, J. R. (2000). A Derivative Security Approach to Setting Crop Revenue Coverage Insurance Premiums. Journal of Agricultural and Resource Economics, No. 25: pp. 159-76.
  • [22] Wang, Wen Bin; Wu, Zi Niu; Wang, Chun Feng; Hu, Rui Feng (2013). Modelling the Spreading Rate of Controlled Communicable Epidemics Through an Entropy-Based Thermodynamic Model. Science China Physics, Mechanics and Astronomy, Vol. 56, No. 11: pp 2143-2150
  • [23] Woo, G. (1999). The Mathematics of Natural Catastrophes. London: Imperial College Press.
  • [24] Wu, Z.N. (2003). Prediction of the Size Distribution of Secondary Ejected Droplets by Crown Splashing of Droplets Impinging on a Solid Wall. Probabilistic Engineering Mechanics, Vol. 18, No. 3.
  • [25] Wu Ziniu; Li Juan; Bai Chenyuan (2017). Scaling Relations of Lognormal Type Growth Process with an Extremal Principle of Entropy. Entropy, Vol. 19, No 56: pp. 1-14.
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