INVESTIGATIONS ON THE ZUBAIR–FAMILY WITH BASELINE GHOSH–BOURGUIGNON’S EXTENDED BURR XII CUMULATIVE SIGMOID. SOME APPLICATIONS

TitleINVESTIGATIONS ON THE ZUBAIR–FAMILY WITH BASELINE GHOSH–BOURGUIGNON’S EXTENDED BURR XII CUMULATIVE SIGMOID. SOME APPLICATIONS
Publication TypeJournal Article
Year of Publication2019
AuthorsRAHNEVA OLGA, TERZIEVA TODORKA, GOLEV ANGEL
JournalNeural, Parallel, and Scientific Computations
Volume27
Issue1
Start Page11
Pagination12
Date Published01/2019
ISSN1061-5369
Keywords41A46, 68N30
Abstract

In this paper we study the one-sided Hausdorff approximation of the shifted Heaviside step function by a class of the Zubair-family of cumulative distribution with baseline Ghosh–Bourguignon’s extended Burr XII c.d.f. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ”saturation” study.

We will illustrate the advances of this new model for approximation and modelling of data for Witty worm for entire world and for USA [1] (see, also [16]) and ”cancer data” (for some details see, [19], [20]).

Numerical examples, illustrating our results are presented using programming environment CAS Mathematica.

URLhttps://acadsol.eu/npsc/articles/27/1/2.pdf
DOI10.12732/npsc.v27i1.2
Refereed DesignationRefereed
Full Text

[1] C. Shannon, D. Moore, The Spread of the Witty Worm, IEEE Security & Privacy , July/August, (2004), 46-50.
[2] Z. Ahmad, The Zubair-G Family of Distributions: Properties and Applications, Annals of Data Science, (2018), doi: 10.1007/s40745-018-0169-9.
[3] N. Kyurkchiev, A. Iliev, A. Rahnev, Comments on a Zubair-G Family of Cumulative Lifetime Distributions. Some Extensions, Communications in Applied Analysis, 23, (1), (2019), 1-20. 
[4] I. Ghosh, M. Bourguignon, A new extended Bur XII distribution, Austrian J. of Statistics, 46, No. 1 (2016), 33-39.
[5] F. Hausdorff, Set Theory (2 ed.) (Chelsea Publ., New York, (1962 [1957]) (Republished by AMS-Chelsea 2005), ISBN: 978-0-821-83835-8.
[6] N. Kyurkchiev, S. Markov, On the Hausdorff distance between the Heaviside step function and Verhulst logistic function, J. Math. Chem., 54, No. 1 (2016), 109-119.
[7] A. Iliev, N. Kyurkchiev, S.Markov, On the Approximation of the step function by some sigmoid functions, Mathematics and Computers in Simulation, 133 (2017), 223-234.
[8] S. Markov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note On the Three-stage Growth Model, Dynamic Systems and Applications, 28, No. 1 (2019), 63-72.
[9] S. Markov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note On the n-stage Growth Model. Overview, Biomath Communications, 5, No. 2 (2018).
[10] N. Kyurkchiev, S. Markov, Sigmoid functions: Some Approximation and Modelling Aspects, LAP LAMBERT Academic Publishing, Saarbrucken (2015), ISBN 978-3-659-76045-7.
[11] N. Kyurkchiev, A. Iliev, Extension of Gompertz-type Equation in Modern Science: 240 Anniversary of the birth of B. Gompertz, LAP LAMBERT Academic Publishing, (2018), ISBN: 978-613-9-90569-0.
[12] N. Kyurkchiev, A. Iliev, S. Markov, Some Techniques for Recurrence Generating of Activation Functions: Some Modeling and Approximation Aspects, LAP LAMBERT Academic Publishing (2017), ISBN: 978-3-330-33143-3.
[13] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Some software reliability models: Approximation and modeling aspects, LAP LAMBERT Academic Publishing (2018), ISBN: 978-613-9-82805-0.
[14] V. Kyurkchiev, A. Malinova, O. Rahneva, P. Kyurkchiev, Some Notes on the Extended Burr XII Software Reliability Model, Int. J. of Pure and Appl. Math., 120 No. 1 (2018), 127-136.
[15] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Nontrivial Models in Debugging Theory (Part 2), LAP LAMBERT Academic Publishing (2018), ISBN: 978-613- 9-87794-2.
[16] N. Kyurkchiev, A. Iliev, A. Rahnev, T. Terzieva, A new analysis of Code Red and Witty worms behavior, Communications in Applied Analysis, 23, No. 2 (2019), 267-285. 
[17] N. Pavlov, N. Kyurkchiev, A. Iliev, A. Rahnev, A Note on the Zubair-G Fam- ily with baseline Lomax Cumulative Distribution Function. Some Applications, International Journal of Pure and Applied Mathematics, 120, No. 3 (2018), 471-486.
[18] N. Kyurkchiev, A. Iliev, A. Rahnev, Some comments on the Weibull-R Family with Baseline Pareto and Lomax Cumulative Sigmoids, International Journal of Pure and Applied Mathematics, 120, No. 3 (2018), 461-469.
[19] M. Vinci, S. Gowan, F. Boxall, L. Patterson, M. Zimmermann, W. Court, C. Lomas, M. Mendila, D. Hardisson, S. Eccles, Advances in establishment and analysis of three-dimensional tumor spheroid-based functional assays for target validation and drug evaluation, BMC Biology, 10 (2012).
[20] A. Antonov, S. Nenov, T. Tsvetkov, Impulsive controllability of tumor growth, Dynamic Systems and Appl., 28, No. 1 (2019), 93-109.
[21] A. Dishliev, K. Dishlieva, S. Nenov, Specific Asymptotic Properties of the Solutions of Impulsive Differential Equations. Methods and Applications, Academic Publications, (2012), available at http://www.acadpubl.eu/ap/node/3.
[22] S. Nenov, Impulsive controllability and optimization problems. Lagrange’smethod and applications, ZAA Zeitschrift f¨ur Analysis und ihre Anwendungen, Heldermann Verlag, Berlin, 17, No. 2 (1998), 501-512.
[23] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Investigations of the K-stage Erlangian software reliability growth model, Int. J. of Pure and Appl. Math., 119, No. 3 (2018), 441-449.
[24] N. Pavlov, A. Golev, A. Rahnev, N. Kyurkchiev, A note on the generalized inverted exponential software reliability model, International Journal of Advanced Research in Computer and Communication Engineering, 7, No. 3 (2018), 484- 487.
[25] N. Pavlov, A. Golev, A. Rahnev, N. Kyurkchiev, Analysis of the Chen’s and Pham’s Software Reliability Models, Cybernetics and Information Technologies, 18, No. 3 (2018), 37-47.
[26] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, On some nonstandard software reliability models, Dynamic Systems and Applications, 27, No. 4 (2018), 757- 771.
[27] N. Pavlov, G. Spasov, A. Rahnev, N. Kyurkchiev, A new class of Gompertz-type software reliability models, International Electronic Journal of Pure and Applied Mathematics, 12, No. 1 (2018), 43-57.
[28] N. Pavlov, G. Spasov, A. Rahnev, N. Kyurkchiev, Some deterministic reliability growth curves for software error detection: Approximation and modeling aspects, International Journal of Pure and Applied Mathematics, 118, No. 3 (2018), 599- 611.
[29] N. Pavlov, A. Golev, A. Rahnev, N. Kyurkchiev, A note on the Yamada-exponential software reliability model, International Journal of Pure and Applied Mathematics , 118, No. 4 (2018), 871-882.
[30] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note on The ”Mean Value” Software Reliability Model, International Journal of Pure and Applied Mathematics , 118, No. 4 (2018), 949-956.
[31] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Transmuted inverse exponential software reliability model, Int. J. of Latest Research in Engineering and Technology, 4, No. 5 (2018), 1-6.
[32] N. Kyurkchiev, A. Iliev, A. Rahnev, Investigations on the G Family with Baseline Burr XII Cumulative Sigmoid, Biomath Communications, 5, No. 2 (2018) (to appear).
[33] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note on Ohbas Inflexion S- shaped Software Reliability Growth Model, Collection of scientific works from conference Mathematics. Informatics. Information Technologies. Application in Education, Pamporovo, Bulgaria, October 10-12, 2018. (to appear)