Marshall-Olkin Exponential Pareto Distribution with Application on Cancer Stem Cells
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 1-7
Received: Dec. 8, 2016;
Accepted: Dec. 27, 2016;
Published: Jan. 24, 2017
Views 2815 Downloads 140
Khairia El-Said El-Nadi, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
L. M. Fatehy, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Nourhan Hamdy Ahmed, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
A Marshall–Olkin variant of exponential Pareto distribution is being introduced in this paper. Some of its statistical functions and numerical characteristics among others characteristics function, moment generalizing function, central moments of real order are derived in the computational series expansion form and various illustrative special cases are discussed. This density function is utilized to model a real data set of cancer stem cells patients. The new distribution provides a better fit than related distributions. The proposed distribution could find applications for instance in the physical and biological sciences, hydrology, medicine, meteorology and engineering.
Khairia El-Said El-Nadi,
L. M. Fatehy,
Nourhan Hamdy Ahmed,
Marshall-Olkin Exponential Pareto Distribution with Application on Cancer Stem Cells, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics.
Vol. 6, No. 5-1,
2017, pp. 1-7.
Marshall, A. M. and Olkin, I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84, 641–652, 1997.
Kareema Abed Al-Kadim and Mohammad Abdalhussain Boshi, Exponential Pareto Distribution, Mathematical theory and modeling, no. 1, volume3, no5, 135-150, 2013
H. M. Srivastava. SOME FOX-WRIGHT GENERALIZED HYPERGEOMETRIC FUNCTIONS AND ASSOCIATED FAMILIES OF CONVOLUTION OPERATORS Applicable Analysis and Discrete Mathematics, 1 (2007), 56–71.
Miller, A. R. and Moskowitz, I. S. Reduction of a class of Fox-Wright Psi functions for certain rational parameters, Comput. Math. Appl. 30, 73–82, 1996.
Nadarajah S., Cordeiro, G. M. and Ortega Edwin, M. M. General results for the beta–modified Weibull distribution J. Statist. Comput. Simulation 81, 121–132, 2011.
Nadarajah, S. and Kotz, S. On a distribution of Leipnik and Pearce, ANZIAM J. 48, 405–407, 2007.
Cordeiro, G. M., Ortega Edwin, M. M. and Cunha D. C. C. The exponentiated generalized class of distributions, J. Data Sci. 11, 1–27, 2013.
Cordeiro, G. M., Ortega Edwin, M. M. and Lemonte, A. J. The exponential–Weibull lifetime distribution. J. Statist. Comput. Simulation 84, 2592–2606, 2014.
Pogany, T. K. and Saxena, R. K. The gamma-Weibull distribution revisited, Anais Acad. Brasil. Ci¸encias 82, 513–520, 2010.
Provost, S. B., Saboor, A. and Ahmad, M. The gamma–Weibull distribution, Pak. J. Statist. 27, 111–113, 2011.
Peng, X. and Yan, Z. Estimation and application for a new extended Weibull distribution, Reliab. Eng. Syst. Safety 121, 34–42, 2014.
Stacy, E. W. A generalization of the gamma distribution, Ann. Math. Stat. 33, 1187–1192, 1962.
Lee, E. and Wang, J. Statistical Methods for Survival Data Analysis. (New York: Wiley &Sons, 2003).
Kilbas, A. A., Srivastava, H. M. and Trujillo, JJ. Theory and Applications of Fractional Differential Equations North-Holland Mathematical Studies, Vol. 204. (Amsterdam: Elsevier (North-Holland) Science Publishers, 2006).
Leipnik, R. B. and Pearce, C. E. M. Independent non–identical five–parameter gamma–Weibull variates and their sums, ANZIAM J. 46, 265–271, 2004.
Luke, Y. L. The Special Functions and Their Approximations Vol. I. (San Diego: Academic Press, 1969.
Nichols, M. D. and Padgett, W. J. A bootstrap control chart for Weibull percentiles, Qual. Reliab. Eng. Int. 22, 141–151, 2006.
Pal, M. and Tiensuwan, M. The beta transmuted Weibull distribution, Austrian Journal of Statistics, 43 (2), 133–149, 2014.
P´olya, Gy. and Szeg˝o G. Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions, Third edition. (Moscow: Nauka, 1978). (in Russian).
Risti´c, M. M. and Balakrishnan, N. The gamma–exponentiated exponential distribution, J. Statist. Comput. Simulation 82 (8), 1191–1206, 2012.
Saboor, A. and Pog´any, T. K. Marshall–Olkin gamma–Weibull distribution with applications, Commun. Stat. Theor. Methods 2014.
Khairia El-Said El-Nadi, Asymptotic formulas for some cylindrical functions and generalized functions, Uspekhi, Math. Nauk, 3, 1969.
Khairia El-Said El-Nadi, Asymptotic methods for non-central Chi square distributions, The Proceeding of the Eight Conference of Statistics and Computer Sciences, April, 15–19, 1972.
Mahmoud M. El-Borai, Khairia El-Said El-Nadi, Osama L. and Hamdy M., Numerical methods for some nonlinear stochastic differential equations, Applied mathematics and computations, 168, 65-75, 2005.
Mahmoud M. El-Borai, Khairia El-Said El-Nadi, Osama L. Mostafa and Hamdy M. Ahmed, Semigroup and some fractional stochastic integral equations, International Journal Pure & Applied Mathematical Sciences, Vol. 3 No. 1, pp. 47-52, 2006.
Khairia El-Said El-Nadi, On some stochastic parabolic differential equations in a Hilbert space, Journal of Applied mathematics and Stochastic Analysis, 2, 167-175, 2005.
Mahmoud M. El-Borai, Khairia El-Said El-Nadi and Hoda A. Foad, On some fractional stochastic delay differential equations, Computers and Mathematics with Applications, 59, 1165–1170, 2010.
Mahmoud M. El-Borai, Khairia El-Said El-Nadi amd Eman G. El-Akabawy, On some fractional evolution equations,, Computers and Mathematics with Applications, 59, 1352–1355, 2010.
Khairia El-Said El-Nadi, Wagdy G. El-Sayed and Ahmed Khdher Qassem, Mathematical model of brain tumor, International Research Journal of Engineering and Technology (IRJET), 590-594, Vol. 2, Aug. 2015.
Khairia El-Said El-Nadi, Wagdy G. El-Sayed and Ahmed Khdher Qassem, On some dynamical systems of controlling tumor growth, International Journal of Applied Science and Mathematics, 146-151, Vol. 2, Issue 5, 2015.