On useful schema in survival analysis after heart attack
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 63-69.

Voir la notice de l'article provenant de la source Library of Science

Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
Keywords: lifetime after heart attack, distribution, Fibonacci number, Lucas number, Pascal triangle
@article{DMPS_2014_34_1-2_a4,
     author = {St\k{e}pniak, Czes{\l}aw},
     title = {On useful schema in survival analysis after heart attack},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {63--69},
     publisher = {mathdoc},
     volume = {34},
     number = {1-2},
     year = {2014},
     zbl = {1327.62502},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a4/}
}
TY  - JOUR
AU  - Stępniak, Czesław
TI  - On useful schema in survival analysis after heart attack
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2014
SP  - 63
EP  - 69
VL  - 34
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a4/
LA  - en
ID  - DMPS_2014_34_1-2_a4
ER  - 
%0 Journal Article
%A Stępniak, Czesław
%T On useful schema in survival analysis after heart attack
%J Discussiones Mathematicae. Probability and Statistics
%D 2014
%P 63-69
%V 34
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a4/
%G en
%F DMPS_2014_34_1-2_a4
Stępniak, Czesław. On useful schema in survival analysis after heart attack. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 63-69. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a4/

[1] H. Belbachir and A. Benmezai, An alternative approach to Cigler's q-Lucas polynomials, Appl. Math. Computat. 226 (2014) 691-698. doi: 10.1016/j.amc.2013.10.009

[2] G.B. Diordjević, Generating functions of the incomplete generalized Fibonacci and generalized Lucas numbers, Fibonacci Quart. 39 (2004) 106-113.

[3] A. Dil and I. Mező, A symmetric algorithm for hyperharmonic and Fibonacci numbers, Appl. Math. Comput. 206 (2008) 942-951. doi: 10.1016/j.amc.2008.10.013

[4] M. El-Mikkawy and T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461. doi: 10.1016/j.amc.2009.12.069

[5] X. Fu and X. Zhou, On matrices related with Fibonacci and Lucas numbers, Appl. Math. Comput. 200 (2008) 96-100. doi: 10.1016/j.amc.2007.10.060

[6] D. Garth, D. Mills and P. Mitchell, Polynomials generated by the Fibonacci sequence, J. Integer. Seq. 10 (2007), Article 07.6.8.

[7] H.H. Gulec, N. Taskara and K. Uslu, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Appl. Math. Comput. 230 (2013) 482-486. doi: 10.1016/j.amc.2013.05.043

[8] J.M. Gutiérrez, M.A. Hernández, P.J. Miana and N. Romero, New identities in the Catalan triangle, J. Math. Anal. Appl. 341 (2008) 52-61. doi: 10.1016/j.jmaa.2007.09.073

[9] P. Hao and S. Zhi-wei, A combinatorial identity with application to Catalan numbers, Discrete Math. 306 (2006) 1921-1940. doi: 10.1016/j.disc.2006.03.050

[10] V.E. Hoggat Jr., Fibonacci and Lucas Numbers, Houghton Miffin (Boston, MA, 1969).

[11] H. Hosoya, Fibonacci triangle, Fibonacci Quart. 14 (1976) 173-178.

[12] B.D. Jones, Comprehensive Medical Terminology, Third Ed. Delmar Publishers (Albany NY, 2008).

[13] S. Kitaev and J. Liese, Harmonic numbers, Catalan's triangle and mesh patterns, Discrete Math. 313 (2013) 1515-1531. doi: 10.1016/j.disc.2013.03.017

[14] E.G. Kocer and N. Touglu, The Binet formulas for the Pell-Lucas p-numbers, Ars Combinatoria 85 (2007) 3-18.

[15] T. Koshy, Fibonacci and Lucas Numbers with Applications (Wiley-Interscience, New York, 2001). doi: 10.1002/9781118033067

[16] T. Koshy, Fibonacci, Lucas, and Pell numbers, and Pascal's triangle, Math. Spectrum 43 (2011) 125-132.

[17] H. Kwong, Two determinants with Fibonacci ad Lucas entries, Appl. Math. Comput. 194 (2007) 568-571. doi: 10.1016/j.amc.2007.04.027

[18] S.-M. Ma, Identities involving generalized Fibonacci-type polynomials, Appl. Math. Comput. 217 (2011) 9297-9301. doi: 10.1016/j.amc.2011.04.012

[19] L. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, Fifth Ed. (Wiley, New York, 1991).

[20] J. Petronilho, Generalized Fibonacci sequences via orthogonal polynomials, Appl. Mat. Comput. 218 (2012) 9819-9824. doi: 10.1016/j.amc.2012.03.053

[21] L.W. Shapiro, A Catalan triangle, Discrete Math. 14 (1976) 83-90. doi: 10.1016/0012-365X(76)90009-1

[22] N. Sloane, On-Line Encyclopedia of Integer Sequences (OEIS), http;//oeis.org.

[23] S. Stanimirović, Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power, Appl. Math. Comput. 217 (2011) 9122-9132. doi: 10.1016/j.amc.2011.03.138

[24] S. Stanimirović, P. Stanimirović, M. Miladinović and A. Ilić, Catalan matrix and related combinatorial identities, Appl. Math. Comput. 215 (2009) 796-805. doi: 10.1016/j.amc.2009.06.003

[25] C. Stępniak, On distribution of waiting time for the first failure followed by a limited length success run, Appl. Math. (Warsaw) (2013) 421-430. doi: 10.4064/am40-4-3

[26] N. Tuglu, E.G. Kocer and A. Stakhov, Bivariate fibonacci like p-polynomials, Appl. Math. Comput. 217 (2011) 10239-10246. doi: 10.1016/j.amc.2011.05.022

[27] S. Vajda, Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood (Chichester 1989).

[28] N.N. Vorobyov, Fibonacci Numbers, Publishing House 'Nauka', Moscow, 1961 (in Russian).

[29] A. Włoch, Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers, Appl. Math. Comput. 219 (2013) 5564-5568. doi: 10.1016/j.amc.2012.11.030

[30] O. Yayenie, A note on generalized Fibonacci sequences, Appl. Math. Comput. 217 (2011) 5603-5611. doi: 10.1016/j.amc.2010.12.038