<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena.</p></abstract>

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena.

A Generalized Logistic Function and Its Applications

Foundations of Management

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Generalized Logistic Function and Its Applications"}

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we...

No (t)	Year	Number of subscriptions per 100 inhabitants, y(t)	Second differences ∆²
1	1992	0.007
2	1993	0.035	0.0378
3	1994	0.101	0.02894
4	1995	0.196	0.27426
5	1996	0.565	1.1828
6	1997	2.117	1.39996
7	1998	5.069	2.29338
8	1999	10.315	2.03268
9	2000	17.593	1.24125
10	2001	26.112	1.67588
11	2002	36.307	−1.0091
12	2003	45.493	5.74175
13	2004	60.421	0.99075
14	2005	76.339	3.94934
15	2006	96.207	−7.6964
16	2007	108.378	−5.5284
17	2008	115.021	−4.3499
18	2009	117.315	3.30763
19	2010	122.915	2.77762
20	2011	131.294	0.67138
21	2012	140.343

No (t)	Year	Smoothed values $y_{t}^{}$ {\rm{y}}_{\rm{t}}^	Second differences ∆²
1	1992	0.007
2	1993	0.021	0.02594
3	1994	0.061	0.027439
4	1995	0.129	0.150848
5	1996	0.347	0.666822
6	1997	1.232	1.033391
7	1998	3.151	1.663384
8	1999	6.733	1.848031
9	2000	12.163	1.544643
10	2001	19.137	1.610262
11	2002	27.722	0.300585
12	2003	36.607	3.021167
13	2004	48.514	2.005957
14	2005	62.427	2.977648
15	2006	79.317	−2.35939
16	2007	93.848	−3.9439
17	2008	104.434	−4.14688
18	2009	110.875	−0.41963
19	2010	116.895	1.178996
20	2011	124.094	0.925189
21	2012	132.219

A Generalized Logistic Function and Its Applications

Pubblicato online: 09 apr 2020

Pagine: 85 - 92

DOI: https://doi.org/10.2478/fman-2020-0007

Parole chiave
generalized logistic function, time series, applications

© 2020 Grzegorz Rządkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Number of subscriptions of mobile telephones per 100 inhabitants in Poland in the years 1992–2012 (Source: ITU, http://www.itu.int)

Exponentially smoothed values for the data of Table 1 (Source: Own elaboration)

A Generalized Logistic Function and Its Applications

Pubblicato online: 09 apr 2020

Pagine: 85 - 92

DOI: https://doi.org/10.2478/fman-2020-0007

Parole chiavegeneralized logistic function, time series, applications

© 2020 Grzegorz Rządkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Number of subscriptions of mobile telephones per 100 inhabitants in Poland in the years 1992–2012 (Source: ITU, http://www.itu.int)

Exponentially smoothed values for the data of Table 1 (Source: Own elaboration)

Parole chiave
generalized logistic function, time series, applications