The 20-60-20 rule

Previous Article
Anisotropy in wavelet-based phase field models
DCDS-B Home
This Issue
Next Article
Impulsive SICNNs with chaotic postsynaptic currents

June 2016, 21(4): 1149-1166. doi: 10.3934/dcdsb.2016.21.1149

The 20-60-20 rule

Piotr Jaworski ^1, and Marcin Pitera ^2,

1.	Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
2.	Institute of Mathematics, Jagiellonian University, S. Łojasiewicza 6, 30-348 Kraków, Poland

Received June 2015 Published March 2016

Abstract
Related Papers

In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio often implies some sort of balance. From practical point of view, this feature leads to efficient management or control. We provide a mathematical illustration, justifying the occurrence of this rule in many real world situations. We show that for any population, which could be described using multivariate normal vector, this fixed ratio leads to a global equilibrium state, when dispersion and linear dependance measurement is considered.

Keywords: 60/20/20 principle, truncated normal distribution, conditional elliptic distribution., the principle of factor sparsity, 20-60-20 rule, law of the vital few, Pareto principle, 20:60:20.

Mathematics Subject Classification: Primary: 60K30, 91B10, 62A86; Secondary: 91B14, 91B5.

Citation: Piotr Jaworski, Marcin Pitera. The 20-60-20 rule. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1149-1166. doi: 10.3934/dcdsb.2016.21.1149

References:

[1]	S. Annunzio, E-leadership - proven techniques for creating an environment of speed and flexibility in the digital economy, Human Resource Management, 40 (2001), 381-383.
[2]	D. Bach, Start Late, Finish Rich: A No-fail Plan for Achieving Financial Freedom at Any Age, Crown Business, 2005.
[3]	B. Bolger, Ten steps to designing an effective incentive program, Employment Relations Today, 31 (2004), 25-33. doi: 10.1002/ert.20003.
[4]	J. Creelman, An act of faith, The TQM Magazine, 5 (1993). doi: 10.1108/EUM0000000003073.
[5]	D. Dupper, School Social Work: Skills and Interventions for Effective Practice, John Wiley & Sons, 2002.
[6]	E. Gómez, M. A. Gómez-Villegas and J. M. Marín, A survey on continuous elliptical vector distributions, Revista matemática complutense, 16 (2003), 345-361. doi: 10.5209/rev_REMA.2003.v16.n1.16889.
[7]	M. A. Grey and A. C. Woodrick, Latinos have revitalized our community: Mexican migration and Anglo responses in Marshalltown, Iowa, in New destinations: Mexican immigration in the United States, (2005), 133-154.
[8]	L. M. Hinman, The impact of the internet on our moral lives in academia, Ethics and information technology, 4 (2002), 31-35.
[9]	P. Jaworski and M. Pitera, On spatial contagion and multivariate GARCH models, Applied Stochastic Models in Business and Industry, 30 (2014), 303-327. doi: 10.1002/asmb.1977.
[10]	N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, John Wiley & Sons, 1994.
[11]	A. Kamiya, F. Makino, and S. Kobayashi, Worker ants' rule-based genetic algorithms dealing with changing environments, in Proceedings of IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications (SMCia/05), 2005, 117-121. doi: 10.1109/SMCIA.2005.1466958.
[12]	R. B. Nelsen, An Introduction to Copulas, Springer, 2006.
[13]	L. Robinson, A summary of diffusion of innovations - Enabling Change., 2009. Available from: , ().
[14]	J. Slagell and J. Holtermann, Climbing peaks and navigating valleys: Managing personnel from high altitude, The Serials Librarian, 52 (2007), 271-275. doi: 10.1300/J123v52n03_04.
[15]	S. A. Tynan, Best behaviors, Management Review, 88 (1999), 58-61.

show all references

References:

[1]	S. Annunzio, E-leadership - proven techniques for creating an environment of speed and flexibility in the digital economy, Human Resource Management, 40 (2001), 381-383.
[2]	D. Bach, Start Late, Finish Rich: A No-fail Plan for Achieving Financial Freedom at Any Age, Crown Business, 2005.
[3]	B. Bolger, Ten steps to designing an effective incentive program, Employment Relations Today, 31 (2004), 25-33. doi: 10.1002/ert.20003.
[4]	J. Creelman, An act of faith, The TQM Magazine, 5 (1993). doi: 10.1108/EUM0000000003073.
[5]	D. Dupper, School Social Work: Skills and Interventions for Effective Practice, John Wiley & Sons, 2002.
[6]	E. Gómez, M. A. Gómez-Villegas and J. M. Marín, A survey on continuous elliptical vector distributions, Revista matemática complutense, 16 (2003), 345-361. doi: 10.5209/rev_REMA.2003.v16.n1.16889.
[7]	M. A. Grey and A. C. Woodrick, Latinos have revitalized our community: Mexican migration and Anglo responses in Marshalltown, Iowa, in New destinations: Mexican immigration in the United States, (2005), 133-154.
[8]	L. M. Hinman, The impact of the internet on our moral lives in academia, Ethics and information technology, 4 (2002), 31-35.
[9]	P. Jaworski and M. Pitera, On spatial contagion and multivariate GARCH models, Applied Stochastic Models in Business and Industry, 30 (2014), 303-327. doi: 10.1002/asmb.1977.
[10]	N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, John Wiley & Sons, 1994.
[11]	A. Kamiya, F. Makino, and S. Kobayashi, Worker ants' rule-based genetic algorithms dealing with changing environments, in Proceedings of IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications (SMCia/05), 2005, 117-121. doi: 10.1109/SMCIA.2005.1466958.
[12]	R. B. Nelsen, An Introduction to Copulas, Springer, 2006.
[13]	L. Robinson, A summary of diffusion of innovations - Enabling Change., 2009. Available from: , ().
[14]	J. Slagell and J. Holtermann, Climbing peaks and navigating valleys: Managing personnel from high altitude, The Serials Librarian, 52 (2007), 271-275. doi: 10.1300/J123v52n03_04.
[15]	S. A. Tynan, Best behaviors, Management Review, 88 (1999), 58-61.

[1]	Carlo Cercignani. The Boltzmann equation in the 20th century. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 83-94. doi: 10.3934/dcds.2009.24.83
[2]	Sascha Kurz. The $[46, 9, 20]_2$ code is unique. Advances in Mathematics of Communications, 2021, 15 (3) : 415-422. doi: 10.3934/amc.2020074
[3]	Peter E. Kloeden, Yuan Lou. Preface for the special issue "20 years of DCDS-B". Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : i-ii. doi: 10.3934/dcdsb.2020372
[4]	Masaaki Harada. New doubly even self-dual codes having minimum weight 20. Advances in Mathematics of Communications, 2020, 14 (1) : 89-96. doi: 10.3934/amc.2020007
[5]	Abraão D. C. Nascimento, Leandro C. Rêgo, Raphaela L. B. A. Nascimento. Compound truncated Poisson normal distribution: Mathematical properties and Moment estimation. Inverse Problems and Imaging, 2019, 13 (4) : 787-803. doi: 10.3934/ipi.2019036
[6]	Josef Hofbauer, Rida Laraki, Jérôme Renault. Preface: Special Issue in Honor of the 60th Birthday of Sylvain Sorin. Journal of Dynamics and Games, 2014, 1 (3) : i-iv. doi: 10.3934/jdg.2014.1.3i
[7]	Luis Alberto Fernández, Mariano Mateos, Cecilia Pola, Fredi Tröltzsch, Enrique Zuazua. Preface: A tribute to professor Eduardo Casas on his 60th birthday. Mathematical Control and Related Fields, 2018, 8 (1) : i-ii. doi: 10.3934/mcrf.201801i
[8]	Hongwei Lou, Qi Lü, Gengsheng Wang, Xu Zhang. Preface: A tribute to professor Jiongmin Yong on his 60th birthday. Mathematical Control and Related Fields, 2018, 8 (3&4) : i-i. doi: 10.3934/mcrf.201803i
[9]	Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6581-6597. doi: 10.3934/dcds.2016085
[10]	Zheng Yin, Ercai Chen. The conditional variational principle for maps with the pseudo-orbit tracing property. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 463-481. doi: 10.3934/dcds.2019019
[11]	Wenqing Hu, Chris Junchi Li. A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4951-4977. doi: 10.3934/dcds.2018216
[12]	María J. Garrido-Atienza, José A. Langa, Pedro Marín Rubio, José Valero. Preface to the special issue in honor of Prof. Tomás Caraballo on occasion of his 60th birthday. Communications on Pure and Applied Analysis, 2020, 19 (4) : i-vi. doi: 10.3934/cpaa.2020080
[13]	Hal L. Smith. Tribute to Horst R. Thieme on the occasion of his 60th birthday. Mathematical Biosciences & Engineering, 2010, 7 (1) : i-iii. doi: 10.3934/mbe.2010.7.1i
[14]	Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367
[15]	H. O. Fattorini. The maximum principle in infinite dimension. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557
[16]	Chiun-Chuan Chen, Li-Chang Hung, Hsiao-Feng Liu. N-barrier maximum principle for degenerate elliptic systems and its application. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 791-821. doi: 10.3934/dcds.2018034
[17]	Tomasz Komorowski, Adam Bobrowski. A quantitative Hopf-type maximum principle for subsolutions of elliptic PDEs. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3495-3502. doi: 10.3934/dcdss.2020248
[18]	Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897
[19]	Giuseppe Capobianco, Tom Winandy, Simon R. Eugster. The principle of virtual work and Hamilton's principle on Galilean manifolds. Journal of Geometric Mechanics, 2021, 13 (2) : 167-193. doi: 10.3934/jgm.2021002
[20]	Robert Stephen Cantrell, Suzanne Lenhart, Yuan Lou, Shigui Ruan. Preface on the special issue of Discrete and Continuous Dynamical Systems- Series B in honor of Chris Cosner on the occasion of his 60th birthday. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : i-ii. doi: 10.3934/dcdsb.2014.19.1i

2020 Impact Factor: 1.327

Tools

Metrics

Other articles
by authors

on AIMS
Piotr Jaworski Marcin Pitera
on Google Scholar
Piotr Jaworski Marcin Pitera

[Back to Top]