Document (#28680)

Author
Egghe, L.
Title
Zipfian and Lotkaian continuous concentration theory
Source
Journal of the American Society for Information Science and Technology. 56(2005) no.9, S.935-945
Year
2005
Abstract
In this article concentration (i.e., inequality) aspects of the functions of Zipf and of Lotka are studied. Since both functions are power laws (i.e., they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf's law and Lotka's law, we prove that Price's law of concentration is equivalent with Zipf's law. A major part of this article is devoted to the development of continuous concentration theory, based an Lorenz curves. The Lorenz curve for power functions is calculated and, based an this, some important concentration measures such as the ones of Gini, Theil, and the variation coefficient. Using Lorenz curves, it is shown that the concentration of a power law increases with its exponent and this result is interpreted in terms of the functions of Zipf and Lotka.
Theme
Informetrie
Object
Zipf-Gesetz
Lotka-Gesetz

Similar documents (author)

1. Egghe, L.: Little science, big science and beyond (1994) 4.71
```4.7136316 = sum of:
4.7136316 = weight(author_txt:egghe in 6883) [ClassicSimilarity], result of:
4.7136316 = fieldWeight in 6883, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.5418105 = idf(docFreq=60, maxDocs=42306)
0.625 = fieldNorm(doc=6883)
```
2. Egghe, L.: Expansion of the field of informetrics : the second special issue (2006) 4.71
```4.7136316 = sum of:
4.7136316 = weight(author_txt:egghe in 7119) [ClassicSimilarity], result of:
4.7136316 = fieldWeight in 7119, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.5418105 = idf(docFreq=60, maxDocs=42306)
0.625 = fieldNorm(doc=7119)
```
3. Egghe, L.: Expansion of the field of informetrics : origins and consequences (2005) 4.71
```4.7136316 = sum of:
4.7136316 = weight(author_txt:egghe in 1979) [ClassicSimilarity], result of:
4.7136316 = fieldWeight in 1979, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.5418105 = idf(docFreq=60, maxDocs=42306)
0.625 = fieldNorm(doc=1979)
```
4. Egghe, L.: ¬The amount of actions needed for shelving and reshelving (1996) 4.71
```4.7136316 = sum of:
4.7136316 = weight(author_txt:egghe in 4463) [ClassicSimilarity], result of:
4.7136316 = fieldWeight in 4463, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.5418105 = idf(docFreq=60, maxDocs=42306)
0.625 = fieldNorm(doc=4463)
```
5. Egghe, L.: Special features of the author - publication relationship and a new explanation of Lotka's law based on convolution theory (1994) 4.71
```4.7136316 = sum of:
4.7136316 = weight(author_txt:egghe in 5137) [ClassicSimilarity], result of:
4.7136316 = fieldWeight in 5137, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.5418105 = idf(docFreq=60, maxDocs=42306)
0.625 = fieldNorm(doc=5137)
```

Similar documents (content)

1. Burrell, Q.L.: On Egghe's version of continuous concentration theory (2006) 0.46
```0.46397433 = sum of:
0.46397433 = product of:
1.6570512 = sum of:
0.02394611 = weight(abstract_txt:article in 904) [ClassicSimilarity], result of:
0.02394611 = score(doc=904,freq=2.0), product of:
0.040154412 = queryWeight, product of:
1.0568547 = boost
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.0098548345 = queryNorm
0.59635067 = fieldWeight in 904, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.0679956 = weight(abstract_txt:coefficient in 904) [ClassicSimilarity], result of:
0.0679956 = score(doc=904,freq=1.0), product of:
0.080518775 = queryWeight, product of:
1.0582353 = boost
7.7208586 = idf(docFreq=50, maxDocs=42306)
0.0098548345 = queryNorm
0.8444689 = fieldWeight in 904, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.7208586 = idf(docFreq=50, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.113359764 = weight(abstract_txt:curve in 904) [ClassicSimilarity], result of:
0.113359764 = score(doc=904,freq=2.0), product of:
0.08985438 = queryWeight, product of:
1.1179008 = boost
8.156177 = idf(docFreq=32, maxDocs=42306)
0.0098548345 = queryNorm
1.2615942 = fieldWeight in 904, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
8.156177 = idf(docFreq=32, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.008737533 = weight(abstract_txt:this in 904) [ClassicSimilarity], result of:
0.008737533 = score(doc=904,freq=1.0), product of:
0.032547865 = queryWeight, product of:
1.3456277 = boost
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.0098548345 = queryNorm
0.2684518 = fieldWeight in 904, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.042921007 = weight(abstract_txt:theory in 904) [ClassicSimilarity], result of:
0.042921007 = score(doc=904,freq=1.0), product of:
0.085453585 = queryWeight, product of:
1.8882498 = boost
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.0098548345 = queryNorm
0.5022727 = fieldWeight in 904, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.45900676 = weight(abstract_txt:lorenz in 904) [ClassicSimilarity], result of:
0.45900676 = score(doc=904,freq=2.0), product of:
0.32922018 = queryWeight, product of:
3.7062738 = boost
9.013627 = idf(docFreq=13, maxDocs=42306)
0.0098548345 = queryNorm
1.3942243 = fieldWeight in 904, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
9.013627 = idf(docFreq=13, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.9410844 = weight(abstract_txt:concentration in 904) [ClassicSimilarity], result of:
0.9410844 = score(doc=904,freq=3.0), product of:
0.6156321 = queryWeight, product of:
7.741824 = boost
8.069165 = idf(docFreq=35, maxDocs=42306)
0.0098548345 = queryNorm
1.5286473 = fieldWeight in 904, product of:
1.7320508 = tf(freq=3.0), with freq of:
3.0 = termFreq=3.0
8.069165 = idf(docFreq=35, maxDocs=42306)
0.109375 = fieldNorm(doc=904)
0.28 = coord(7/25)
```
2. Rousseau, R.: On Egghe's construction of Lorenz curves (2007) 0.44
```0.43984824 = sum of:
0.43984824 = product of:
2.1992412 = sum of:
0.16031492 = weight(abstract_txt:curve in 2522) [ClassicSimilarity], result of:
0.16031492 = score(doc=2522,freq=1.0), product of:
0.08985438 = queryWeight, product of:
1.1179008 = boost
8.156177 = idf(docFreq=32, maxDocs=42306)
0.0098548345 = queryNorm
1.7841636 = fieldWeight in 2522, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
8.156177 = idf(docFreq=32, maxDocs=42306)
0.21875 = fieldNorm(doc=2522)
0.08584201 = weight(abstract_txt:theory in 2522) [ClassicSimilarity], result of:
0.08584201 = score(doc=2522,freq=1.0), product of:
0.085453585 = queryWeight, product of:
1.8882498 = boost
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.0098548345 = queryNorm
1.0045455 = fieldWeight in 2522, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.21875 = fieldNorm(doc=2522)
0.21727985 = weight(abstract_txt:continuous in 2522) [ClassicSimilarity], result of:
0.21727985 = score(doc=2522,freq=1.0), product of:
0.13864778 = queryWeight, product of:
1.9638356 = boost
7.1640477 = idf(docFreq=88, maxDocs=42306)
0.0098548345 = queryNorm
1.5671355 = fieldWeight in 2522, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
7.1640477 = idf(docFreq=88, maxDocs=42306)
0.21875 = fieldNorm(doc=2522)
0.6491336 = weight(abstract_txt:lorenz in 2522) [ClassicSimilarity], result of:
0.6491336 = score(doc=2522,freq=1.0), product of:
0.32922018 = queryWeight, product of:
3.7062738 = boost
9.013627 = idf(docFreq=13, maxDocs=42306)
0.0098548345 = queryNorm
1.971731 = fieldWeight in 2522, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
9.013627 = idf(docFreq=13, maxDocs=42306)
0.21875 = fieldNorm(doc=2522)
1.0866706 = weight(abstract_txt:concentration in 2522) [ClassicSimilarity], result of:
1.0866706 = score(doc=2522,freq=1.0), product of:
0.6156321 = queryWeight, product of:
7.741824 = boost
8.069165 = idf(docFreq=35, maxDocs=42306)
0.0098548345 = queryNorm
1.7651299 = fieldWeight in 2522, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
8.069165 = idf(docFreq=35, maxDocs=42306)
0.21875 = fieldNorm(doc=2522)
0.2 = coord(5/25)
```
3. Egghe, L.: ¬The power of power laws and an interpretation of Lotkaian informetric systems as self-similar fractals (2005) 0.29
```0.29294154 = sum of:
0.29294154 = product of:
0.8137265 = sum of:
0.00967569 = weight(abstract_txt:article in 4467) [ClassicSimilarity], result of:
0.00967569 = score(doc=4467,freq=1.0), product of:
0.040154412 = queryWeight, product of:
1.0568547 = boost
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.0098548345 = queryNorm
0.24096206 = fieldWeight in 4467, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.07492593 = weight(abstract_txt:lotka's in 4467) [ClassicSimilarity], result of:
0.07492593 = score(doc=4467,freq=2.0), product of:
0.09901024 = queryWeight, product of:
1.1734747 = boost
8.561642 = idf(docFreq=21, maxDocs=42306)
0.0098548345 = queryNorm
0.75674933 = fieldWeight in 4467, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
8.561642 = idf(docFreq=21, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.059115164 = weight(abstract_txt:exponent in 4467) [ClassicSimilarity], result of:
0.059115164 = score(doc=4467,freq=1.0), product of:
0.106512666 = queryWeight, product of:
1.2171224 = boost
8.8800955 = idf(docFreq=15, maxDocs=42306)
0.0098548345 = queryNorm
0.55500597 = fieldWeight in 4467, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
8.8800955 = idf(docFreq=15, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.06691841 = weight(abstract_txt:lotkaian in 4467) [ClassicSimilarity], result of:
0.06691841 = score(doc=4467,freq=1.0), product of:
0.115690865 = queryWeight, product of:
1.2684788 = boost
9.254789 = idf(docFreq=10, maxDocs=42306)
0.0098548345 = queryNorm
0.57842433 = fieldWeight in 4467, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
9.254789 = idf(docFreq=10, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.008647915 = weight(abstract_txt:this in 4467) [ClassicSimilarity], result of:
0.008647915 = score(doc=4467,freq=3.0), product of:
0.032547865 = queryWeight, product of:
1.3456277 = boost
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.0098548345 = queryNorm
0.26569837 = fieldWeight in 4467, product of:
1.7320508 = tf(freq=3.0), with freq of:
3.0 = termFreq=3.0
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.18536982 = weight(abstract_txt:laws in 4467) [ClassicSimilarity], result of:
0.18536982 = score(doc=4467,freq=4.0), product of:
0.20732345 = queryWeight, product of:
2.941159 = boost
7.1528745 = idf(docFreq=89, maxDocs=42306)
0.0098548345 = queryNorm
0.8941093 = fieldWeight in 4467, product of:
2.0 = tf(freq=4.0), with freq of:
4.0 = termFreq=4.0
7.1528745 = idf(docFreq=89, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.079728484 = weight(abstract_txt:functions in 4467) [ClassicSimilarity], result of:
0.079728484 = score(doc=4467,freq=2.0), product of:
0.16381525 = queryWeight, product of:
3.018845 = boost
5.506355 = idf(docFreq=466, maxDocs=42306)
0.0098548345 = queryNorm
0.48669758 = fieldWeight in 4467, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
5.506355 = idf(docFreq=466, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.1144861 = weight(abstract_txt:power in 4467) [ClassicSimilarity], result of:
0.1144861 = score(doc=4467,freq=3.0), product of:
0.18214478 = queryWeight, product of:
3.1832592 = boost
5.8062453 = idf(docFreq=345, maxDocs=42306)
0.0098548345 = queryNorm
0.6285445 = fieldWeight in 4467, product of:
1.7320508 = tf(freq=3.0), with freq of:
3.0 = termFreq=3.0
5.8062453 = idf(docFreq=345, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.21485895 = weight(abstract_txt:lotka in 4467) [ClassicSimilarity], result of:
0.21485895 = score(doc=4467,freq=2.0), product of:
0.28822702 = queryWeight, product of:
3.4678607 = boost
8.433808 = idf(docFreq=24, maxDocs=42306)
0.0098548345 = queryNorm
0.7454504 = fieldWeight in 4467, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
8.433808 = idf(docFreq=24, maxDocs=42306)
0.0625 = fieldNorm(doc=4467)
0.36 = coord(9/25)
```
4. Egghe, L.: Relations between the continuous and the discrete Lotka power function (2005) 0.27
```0.26967588 = sum of:
0.26967588 = product of:
0.9631281 = sum of:
0.08364802 = weight(abstract_txt:lotkaian in 4465) [ClassicSimilarity], result of:
0.08364802 = score(doc=4465,freq=1.0), product of:
0.115690865 = queryWeight, product of:
1.2684788 = boost
9.254789 = idf(docFreq=10, maxDocs=42306)
0.0098548345 = queryNorm
0.72303045 = fieldWeight in 4465, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
9.254789 = idf(docFreq=10, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.006241095 = weight(abstract_txt:this in 4465) [ClassicSimilarity], result of:
0.006241095 = score(doc=4465,freq=1.0), product of:
0.032547865 = queryWeight, product of:
1.3456277 = boost
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.0098548345 = queryNorm
0.19175129 = fieldWeight in 4465, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
2.4544165 = idf(docFreq=9879, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.030657863 = weight(abstract_txt:theory in 4465) [ClassicSimilarity], result of:
0.030657863 = score(doc=4465,freq=1.0), product of:
0.085453585 = queryWeight, product of:
1.8882498 = boost
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.0098548345 = queryNorm
0.35876626 = fieldWeight in 4465, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.19008029 = weight(abstract_txt:continuous in 4465) [ClassicSimilarity], result of:
0.19008029 = score(doc=4465,freq=6.0), product of:
0.13864778 = queryWeight, product of:
1.9638356 = boost
7.1640477 = idf(docFreq=88, maxDocs=42306)
0.0098548345 = queryNorm
1.370958 = fieldWeight in 4465, product of:
2.4494898 = tf(freq=6.0), with freq of:
6.0 = termFreq=6.0
7.1640477 = idf(docFreq=88, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.07047069 = weight(abstract_txt:functions in 4465) [ClassicSimilarity], result of:
0.07047069 = score(doc=4465,freq=1.0), product of:
0.16381525 = queryWeight, product of:
3.018845 = boost
5.506355 = idf(docFreq=466, maxDocs=42306)
0.0098548345 = queryNorm
0.43018398 = fieldWeight in 4465, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
5.506355 = idf(docFreq=466, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.116846874 = weight(abstract_txt:power in 4465) [ClassicSimilarity], result of:
0.116846874 = score(doc=4465,freq=2.0), product of:
0.18214478 = queryWeight, product of:
3.1832592 = boost
5.8062453 = idf(docFreq=345, maxDocs=42306)
0.0098548345 = queryNorm
0.6415055 = fieldWeight in 4465, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
5.8062453 = idf(docFreq=345, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.46518326 = weight(abstract_txt:lotka in 4465) [ClassicSimilarity], result of:
0.46518326 = score(doc=4465,freq=6.0), product of:
0.28822702 = queryWeight, product of:
3.4678607 = boost
8.433808 = idf(docFreq=24, maxDocs=42306)
0.0098548345 = queryNorm
1.6139474 = fieldWeight in 4465, product of:
2.4494898 = tf(freq=6.0), with freq of:
6.0 = termFreq=6.0
8.433808 = idf(docFreq=24, maxDocs=42306)
0.078125 = fieldNorm(doc=4465)
0.28 = coord(7/25)
```
5. Burrell, Q.L.: Egghe's construction of Lorenz curves resolved (2007) 0.17
```0.17157605 = sum of:
0.17157605 = product of:
0.85788023 = sum of:
0.012094612 = weight(abstract_txt:article in 2625) [ClassicSimilarity], result of:
0.012094612 = score(doc=2625,freq=1.0), product of:
0.040154412 = queryWeight, product of:
1.0568547 = boost
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.0098548345 = queryNorm
0.30120257 = fieldWeight in 2625, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
3.855393 = idf(docFreq=2433, maxDocs=42306)
0.078125 = fieldNorm(doc=2625)
0.099169135 = weight(abstract_txt:curve in 2625) [ClassicSimilarity], result of:
0.099169135 = score(doc=2625,freq=3.0), product of:
0.08985438 = queryWeight, product of:
1.1179008 = boost
8.156177 = idf(docFreq=32, maxDocs=42306)
0.0098548345 = queryNorm
1.103665 = fieldWeight in 2625, product of:
1.7320508 = tf(freq=3.0), with freq of:
3.0 = termFreq=3.0
8.156177 = idf(docFreq=32, maxDocs=42306)
0.078125 = fieldNorm(doc=2625)
0.030657863 = weight(abstract_txt:theory in 2625) [ClassicSimilarity], result of:
0.030657863 = score(doc=2625,freq=1.0), product of:
0.085453585 = queryWeight, product of:
1.8882498 = boost
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.0098548345 = queryNorm
0.35876626 = fieldWeight in 2625, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
4.592208 = idf(docFreq=1164, maxDocs=42306)
0.078125 = fieldNorm(doc=2625)
0.32786196 = weight(abstract_txt:lorenz in 2625) [ClassicSimilarity], result of:
0.32786196 = score(doc=2625,freq=2.0), product of:
0.32922018 = queryWeight, product of:
3.7062738 = boost
9.013627 = idf(docFreq=13, maxDocs=42306)
0.0098548345 = queryNorm
0.99587446 = fieldWeight in 2625, product of:
1.4142135 = tf(freq=2.0), with freq of:
2.0 = termFreq=2.0
9.013627 = idf(docFreq=13, maxDocs=42306)
0.078125 = fieldNorm(doc=2625)
0.38809666 = weight(abstract_txt:concentration in 2625) [ClassicSimilarity], result of:
0.38809666 = score(doc=2625,freq=1.0), product of:
0.6156321 = queryWeight, product of:
7.741824 = boost
8.069165 = idf(docFreq=35, maxDocs=42306)
0.0098548345 = queryNorm
0.6304035 = fieldWeight in 2625, product of:
1.0 = tf(freq=1.0), with freq of:
1.0 = termFreq=1.0
8.069165 = idf(docFreq=35, maxDocs=42306)
0.078125 = fieldNorm(doc=2625)
0.2 = coord(5/25)
```