Document (#40700)

Author

Smolinsky, L.J.

Title

Discrete power law with exponential cutoff and Lotka's law

Source

Journal of the Association for Information Science and Technology. 68(2017) no.7, S.1792-1795

Year

2017

Series

Brief communication

Abstract

One of the first bibliometric laws appeared in Alfred J. Lotka's 1926 examination of author productivity in chemistry and physics. The result was a productivity distribution described by a power law. In this paper, Lotka's original data on author productivity in chemistry are reconsidered. We define a discrete power law with exponential cutoff, test Lotka's data, and compare the fit to the discrete power law.

Content

Vgl.: http://onlinelibrary.wiley.com/doi/10.1002/asi.23763/full.

Theme

Informetrie

Object

Lotka-Gesetz

Similar documents (content)

1. Egghe, L.: ¬The power of power laws and an interpretation of Lotkaian informetric systems as self-similar fractals (2005) 0.32

   0.32137102 = sum of:
     0.32137102 = product of:
       1.1477536 = sum of:
         0.0053296383 = weight(abstract_txt:with in 4466) [ClassicSimilarity], result of:
           0.0053296383 = score(doc=4466,freq=2.0), product of:
             0.02415649 = queryWeight, product of:
               1.0031842 = boost
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.009646822 = queryNorm
             0.22062966 = fieldWeight in 4466, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.08809371 = weight(abstract_txt:laws in 4466) [ClassicSimilarity], result of:
           0.08809371 = score(doc=4466,freq=4.0), product of:
             0.09874428 = queryWeight, product of:
               1.4341835 = boost
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.009646822 = queryNorm
             0.8921399 = fieldWeight in 4466, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.11248697 = weight(abstract_txt:1926 in 4466) [ClassicSimilarity], result of:
           0.11248697 = score(doc=4466,freq=1.0), product of:
             0.18448886 = queryWeight, product of:
               1.960351 = boost
               9.755557 = idf(docFreq=6, maxDocs=44421)
               0.009646822 = queryNorm
             0.6097223 = fieldWeight in 4466, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.755557 = idf(docFreq=6, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.16196102 = weight(abstract_txt:exponential in 4466) [ClassicSimilarity], result of:
           0.16196102 = score(doc=4466,freq=2.0), product of:
             0.23523882 = queryWeight, product of:
               3.1305327 = boost
               7.7894444 = idf(docFreq=49, maxDocs=44421)
               0.009646822 = queryNorm
             0.6884961 = fieldWeight in 4466, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.7894444 = idf(docFreq=49, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.15878418 = weight(abstract_txt:power in 4466) [ClassicSimilarity], result of:
           0.15878418 = score(doc=4466,freq=3.0), product of:
             0.25551698 = queryWeight, product of:
               4.614117 = boost
               5.7404623 = idf(docFreq=387, maxDocs=44421)
               0.009646822 = queryNorm
             0.62142324 = fieldWeight in 4466, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.7404623 = idf(docFreq=387, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.18358113 = weight(abstract_txt:discrete in 4466) [ClassicSimilarity], result of:
           0.18358113 = score(doc=4466,freq=1.0), product of:
             0.3688313 = queryWeight, product of:
               4.8009067 = boost
               7.963798 = idf(docFreq=41, maxDocs=44421)
               0.009646822 = queryNorm
             0.49773738 = fieldWeight in 4466, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.963798 = idf(docFreq=41, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
         0.4375169 = weight(abstract_txt:lotka's in 4466) [ClassicSimilarity], result of:
           0.4375169 = score(doc=4466,freq=2.0), product of:
             0.5748774 = queryWeight, product of:
               6.9209604 = boost
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.009646822 = queryNorm
             0.76106125 = fieldWeight in 4466, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.0625 = fieldNorm(doc=4466)
       0.28 = coord(7/25)
   

2. Kretschmer, H.; Kretschmer, T.: Well-ordered collaboration structures of co-author pairs in journals (2006) 0.19

   0.19120176 = sum of:
     0.19120176 = product of:
       0.796674 = sum of:
         0.0053296383 = weight(abstract_txt:with in 150) [ClassicSimilarity], result of:
           0.0053296383 = score(doc=150,freq=2.0), product of:
             0.02415649 = queryWeight, product of:
               1.0031842 = boost
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.009646822 = queryNorm
             0.22062966 = fieldWeight in 150, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
         0.07357442 = weight(abstract_txt:distribution in 150) [ClassicSimilarity], result of:
           0.07357442 = score(doc=150,freq=12.0), product of:
             0.06071921 = queryWeight, product of:
               1.1246356 = boost
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.009646822 = queryNorm
             1.2117156 = fieldWeight in 150, product of:
               3.4641016 = tf(freq=12.0), with freq of:
                 12.0 = termFreq=12.0
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
         0.01265645 = weight(abstract_txt:data in 150) [ClassicSimilarity], result of:
           0.01265645 = score(doc=150,freq=2.0), product of:
             0.042997506 = queryWeight, product of:
               1.3383983 = boost
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.009646822 = queryNorm
             0.29435313 = fieldWeight in 150, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
         0.044046856 = weight(abstract_txt:laws in 150) [ClassicSimilarity], result of:
           0.044046856 = score(doc=150,freq=1.0), product of:
             0.09874428 = queryWeight, product of:
               1.4341835 = boost
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.009646822 = queryNorm
             0.44606996 = fieldWeight in 150, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
         0.042324323 = weight(abstract_txt:author in 150) [ClassicSimilarity], result of:
           0.042324323 = score(doc=150,freq=2.0), product of:
             0.09615282 = queryWeight, product of:
               2.00145 = boost
               4.980042 = idf(docFreq=829, maxDocs=44421)
               0.009646822 = queryNorm
             0.44017768 = fieldWeight in 150, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.980042 = idf(docFreq=829, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
         0.61874235 = weight(abstract_txt:lotka's in 150) [ClassicSimilarity], result of:
           0.61874235 = score(doc=150,freq=4.0), product of:
             0.5748774 = queryWeight, product of:
               6.9209604 = boost
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.009646822 = queryNorm
             1.0763031 = fieldWeight in 150, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.0625 = fieldNorm(doc=150)
       0.24 = coord(6/25)
   

3. Joshi, A.N.; Maheshwarappa, B.S.: Studies in scientific productivity : a review of literature (1996) 0.19

   0.18986471 = sum of:
     0.18986471 = product of:
       0.94932353 = sum of:
         0.031858657 = weight(abstract_txt:distribution in 405) [ClassicSimilarity], result of:
           0.031858657 = score(doc=405,freq=1.0), product of:
             0.06071921 = queryWeight, product of:
               1.1246356 = boost
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.009646822 = queryNorm
             0.52468824 = fieldWeight in 405, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.09375 = fieldNorm(doc=405)
         0.04264684 = weight(abstract_txt:bibliometric in 405) [ClassicSimilarity], result of:
           0.04264684 = score(doc=405,freq=1.0), product of:
             0.07375063 = queryWeight, product of:
               1.2394575 = boost
               6.168078 = idf(docFreq=252, maxDocs=44421)
               0.009646822 = queryNorm
             0.5782573 = fieldWeight in 405, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.168078 = idf(docFreq=252, maxDocs=44421)
               0.09375 = fieldNorm(doc=405)
         0.16873045 = weight(abstract_txt:1926 in 405) [ClassicSimilarity], result of:
           0.16873045 = score(doc=405,freq=1.0), product of:
             0.18448886 = queryWeight, product of:
               1.960351 = boost
               9.755557 = idf(docFreq=6, maxDocs=44421)
               0.009646822 = queryNorm
             0.91458344 = fieldWeight in 405, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.755557 = idf(docFreq=6, maxDocs=44421)
               0.09375 = fieldNorm(doc=405)
         0.2420308 = weight(abstract_txt:productivity in 405) [ClassicSimilarity], result of:
           0.2420308 = score(doc=405,freq=2.0), product of:
             0.26860783 = queryWeight, product of:
               4.097026 = boost
               6.7961926 = idf(docFreq=134, maxDocs=44421)
               0.009646822 = queryNorm
             0.9010564 = fieldWeight in 405, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.7961926 = idf(docFreq=134, maxDocs=44421)
               0.09375 = fieldNorm(doc=405)
         0.46405676 = weight(abstract_txt:lotka's in 405) [ClassicSimilarity], result of:
           0.46405676 = score(doc=405,freq=1.0), product of:
             0.5748774 = queryWeight, product of:
               6.9209604 = boost
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.009646822 = queryNorm
             0.8072274 = fieldWeight in 405, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.09375 = fieldNorm(doc=405)
       0.2 = coord(5/25)
   

4. Newby, G.B.; Greenberg, J.; Jones, P.: Open source software development and Lotka's law : bibliometric patterns in programming (2003) 0.18

   0.18419631 = sum of:
     0.18419631 = product of:
       0.65784395 = sum of:
         0.006662048 = weight(abstract_txt:with in 140) [ClassicSimilarity], result of:
           0.006662048 = score(doc=140,freq=2.0), product of:
             0.02415649 = queryWeight, product of:
               1.0031842 = boost
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.009646822 = queryNorm
             0.2757871 = fieldWeight in 140, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.027518187 = weight(abstract_txt:test in 140) [ClassicSimilarity], result of:
           0.027518187 = score(doc=140,freq=2.0), product of:
             0.049358867 = queryWeight, product of:
               1.0139846 = boost
               5.046027 = idf(docFreq=776, maxDocs=44421)
               0.009646822 = queryNorm
             0.5575125 = fieldWeight in 140, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.046027 = idf(docFreq=776, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.037545785 = weight(abstract_txt:distribution in 140) [ClassicSimilarity], result of:
           0.037545785 = score(doc=140,freq=2.0), product of:
             0.06071921 = queryWeight, product of:
               1.1246356 = boost
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.009646822 = queryNorm
             0.618351 = fieldWeight in 140, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.019376153 = weight(abstract_txt:data in 140) [ClassicSimilarity], result of:
           0.019376153 = score(doc=140,freq=3.0), product of:
             0.042997506 = queryWeight, product of:
               1.3383983 = boost
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.009646822 = queryNorm
             0.45063436 = fieldWeight in 140, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.03740977 = weight(abstract_txt:author in 140) [ClassicSimilarity], result of:
           0.03740977 = score(doc=140,freq=1.0), product of:
             0.09615282 = queryWeight, product of:
               2.00145 = boost
               4.980042 = idf(docFreq=829, maxDocs=44421)
               0.009646822 = queryNorm
             0.38906577 = fieldWeight in 140, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.980042 = idf(docFreq=829, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.14261802 = weight(abstract_txt:productivity in 140) [ClassicSimilarity], result of:
           0.14261802 = score(doc=140,freq=1.0), product of:
             0.26860783 = queryWeight, product of:
               4.097026 = boost
               6.7961926 = idf(docFreq=134, maxDocs=44421)
               0.009646822 = queryNorm
             0.5309526 = fieldWeight in 140, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.7961926 = idf(docFreq=134, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
         0.38671395 = weight(abstract_txt:lotka's in 140) [ClassicSimilarity], result of:
           0.38671395 = score(doc=140,freq=1.0), product of:
             0.5748774 = queryWeight, product of:
               6.9209604 = boost
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.009646822 = queryNorm
             0.67268944 = fieldWeight in 140, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.078125 = fieldNorm(doc=140)
       0.28 = coord(7/25)
   

5. Arsenault, C.: Aggregation consistency and frequency of Chinese words and characters (2006) 0.18

   0.17646699 = sum of:
     0.17646699 = product of:
       0.63023925 = sum of:
         0.0053296383 = weight(abstract_txt:with in 734) [ClassicSimilarity], result of:
           0.0053296383 = score(doc=734,freq=2.0), product of:
             0.02415649 = queryWeight, product of:
               1.0031842 = boost
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.009646822 = queryNorm
             0.22062966 = fieldWeight in 734, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4961398 = idf(docFreq=9949, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.015566637 = weight(abstract_txt:test in 734) [ClassicSimilarity], result of:
           0.015566637 = score(doc=734,freq=1.0), product of:
             0.049358867 = queryWeight, product of:
               1.0139846 = boost
               5.046027 = idf(docFreq=776, maxDocs=44421)
               0.009646822 = queryNorm
             0.3153767 = fieldWeight in 734, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.046027 = idf(docFreq=776, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.042478207 = weight(abstract_txt:distribution in 734) [ClassicSimilarity], result of:
           0.042478207 = score(doc=734,freq=4.0), product of:
             0.06071921 = queryWeight, product of:
               1.1246356 = boost
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.009646822 = queryNorm
             0.6995843 = fieldWeight in 734, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               5.5966744 = idf(docFreq=447, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.040207826 = weight(abstract_txt:bibliometric in 734) [ClassicSimilarity], result of:
           0.040207826 = score(doc=734,freq=2.0), product of:
             0.07375063 = queryWeight, product of:
               1.2394575 = boost
               6.168078 = idf(docFreq=252, maxDocs=44421)
               0.009646822 = queryNorm
             0.5451862 = fieldWeight in 734, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.168078 = idf(docFreq=252, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.026848387 = weight(abstract_txt:data in 734) [ClassicSimilarity], result of:
           0.026848387 = score(doc=734,freq=9.0), product of:
             0.042997506 = queryWeight, product of:
               1.3383983 = boost
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.009646822 = queryNorm
             0.6244173 = fieldWeight in 734, product of:
               3.0 = tf(freq=9.0), with freq of:
                 9.0 = termFreq=9.0
               3.3302255 = idf(docFreq=4320, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.06229166 = weight(abstract_txt:laws in 734) [ClassicSimilarity], result of:
           0.06229166 = score(doc=734,freq=2.0), product of:
             0.09874428 = queryWeight, product of:
               1.4341835 = boost
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.009646822 = queryNorm
             0.63083816 = fieldWeight in 734, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.1371193 = idf(docFreq=95, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
         0.4375169 = weight(abstract_txt:lotka's in 734) [ClassicSimilarity], result of:
           0.4375169 = score(doc=734,freq=2.0), product of:
             0.5748774 = queryWeight, product of:
               6.9209604 = boost
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.009646822 = queryNorm
             0.76106125 = fieldWeight in 734, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.610425 = idf(docFreq=21, maxDocs=44421)
               0.0625 = fieldNorm(doc=734)
       0.28 = coord(7/25)