Document (#34127)

Author

Burrell, Q.L.

Title

Extending Lotkaian informetrics

Source

Information processing and management. 44(2008) no.5, S.1794-1807

Year

2008

Abstract

The continuous version of the Lotka distribution, more generally referred to outside of informetrics as the Pareto distribution, has long enjoyed a central position in the theoretical development of informetrics despite several reported drawbacks in modelling empirical data distributions, most particularly that the inverse power form seems mainly to be evident only in the upper tails. We give a number of published examples graphically illustrating this shortcoming. In seeking to overcome this, we here draw attention to an intuitively reasonable generalization of the Pareto distribution, namely the Pareto type II distribution, of which we consider two versions. We describe its basic properties and some statistical features together with concentration aspects and argue that, at least in qualitative terms, it is better able to describe many observed informetric phenomena over the full range of the distribution. Suggestions for further investigations, including truncated and time-dependent versions, are also given.

Theme

Informetrie

Object

Lotka-Gesetz

Similar documents (author)

1. Burrell, Q.L.: Will this paper ever be cited? (2002) 5.66

   5.661144 = sum of:
     5.661144 = weight(author_txt:burrell in 3183) [ClassicSimilarity], result of:
       5.661144 = fieldWeight in 3183, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.05783 = idf(docFreq=13, maxDocs=44218)
         0.625 = fieldNorm(doc=3183)
   

2. Burrell, Q.L.: Fitting Lotka's law : some cautionary observations on a recent paper by Newby et al. (2003) (2004) 5.66

   5.661144 = sum of:
     5.661144 = weight(author_txt:burrell in 6235) [ClassicSimilarity], result of:
       5.661144 = fieldWeight in 6235, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.05783 = idf(docFreq=13, maxDocs=44218)
         0.625 = fieldNorm(doc=6235)
   

3. Burrell, Q.L.: "Ambiguity" ans scientometric measurement : a dissenting view (2001) 5.66

   5.661144 = sum of:
     5.661144 = weight(author_txt:burrell in 6981) [ClassicSimilarity], result of:
       5.661144 = fieldWeight in 6981, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.05783 = idf(docFreq=13, maxDocs=44218)
         0.625 = fieldNorm(doc=6981)
   

4. Burrell, Q.L.: "Type/Token-Taken" informetrics : Some comments and further examples (2003) 5.66

   5.661144 = sum of:
     5.661144 = weight(author_txt:burrell in 2116) [ClassicSimilarity], result of:
       5.661144 = fieldWeight in 2116, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.05783 = idf(docFreq=13, maxDocs=44218)
         0.625 = fieldNorm(doc=2116)
   

5. Burrell, Q.L.: Measuring similarity of concentration between different informetric distributions : two new approaches (2005) 5.66

   5.661144 = sum of:
     5.661144 = weight(author_txt:burrell in 3410) [ClassicSimilarity], result of:
       5.661144 = fieldWeight in 3410, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.05783 = idf(docFreq=13, maxDocs=44218)
         0.625 = fieldNorm(doc=3410)
   

Similar documents (content)

1. Burrell, Q.L.: Formulae for the h-index : a lack of robustness in Lotkaian informetrics? (2013) 0.25

   0.24573924 = sum of:
     0.24573924 = product of:
       1.0239135 = sum of:
         0.06187934 = weight(abstract_txt:upper in 977) [ClassicSimilarity], result of:
           0.06187934 = score(doc=977,freq=1.0), product of:
             0.12651536 = queryWeight, product of:
               1.1034967 = boost
               7.825686 = idf(docFreq=47, maxDocs=44218)
               0.014650412 = queryNorm
             0.48910537 = fieldWeight in 977, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.825686 = idf(docFreq=47, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
         0.13627651 = weight(abstract_txt:lotka in 977) [ClassicSimilarity], result of:
           0.13627651 = score(doc=977,freq=3.0), product of:
             0.1484863 = queryWeight, product of:
               1.1954807 = boost
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.014650412 = queryNorm
             0.91777164 = fieldWeight in 977, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
         0.10382121 = weight(abstract_txt:lotkaian in 977) [ClassicSimilarity], result of:
           0.10382121 = score(doc=977,freq=1.0), product of:
             0.17863649 = queryWeight, product of:
               1.3112469 = boost
               9.298992 = idf(docFreq=10, maxDocs=44218)
               0.014650412 = queryNorm
             0.581187 = fieldWeight in 977, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.298992 = idf(docFreq=10, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
         0.18135703 = weight(abstract_txt:informetrics in 977) [ClassicSimilarity], result of:
           0.18135703 = score(doc=977,freq=1.0), product of:
             0.37368828 = queryWeight, product of:
               3.284844 = boost
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.014650412 = queryNorm
             0.48531634 = fieldWeight in 977, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
         0.19600831 = weight(abstract_txt:distribution in 977) [ClassicSimilarity], result of:
           0.19600831 = score(doc=977,freq=3.0), product of:
             0.3235281 = queryWeight, product of:
               3.9458485 = boost
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.014650412 = queryNorm
             0.6058463 = fieldWeight in 977, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
         0.34457114 = weight(abstract_txt:pareto in 977) [ClassicSimilarity], result of:
           0.34457114 = score(doc=977,freq=1.0), product of:
             0.5732435 = queryWeight, product of:
               4.0684557 = boost
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.014650412 = queryNorm
             0.6010904 = fieldWeight in 977, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.0625 = fieldNorm(doc=977)
       0.24 = coord(6/25)
   

2. Shan, S.: On the generalized Zipf distribution : part I (2005) 0.15

   0.1543731 = sum of:
     0.1543731 = product of:
       0.7718654 = sum of:
         0.09208728 = weight(abstract_txt:informetric in 1061) [ClassicSimilarity], result of:
           0.09208728 = score(doc=1061,freq=1.0), product of:
             0.12584956 = queryWeight, product of:
               1.1005892 = boost
               7.805067 = idf(docFreq=48, maxDocs=44218)
               0.014650412 = queryNorm
             0.73172504 = fieldWeight in 1061, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.805067 = idf(docFreq=48, maxDocs=44218)
               0.09375 = fieldNorm(doc=1061)
         0.10800689 = weight(abstract_txt:generalization in 1061) [ClassicSimilarity], result of:
           0.10800689 = score(doc=1061,freq=1.0), product of:
             0.13996504 = queryWeight, product of:
               1.1606711 = boost
               8.231152 = idf(docFreq=31, maxDocs=44218)
               0.014650412 = queryNorm
             0.77167046 = fieldWeight in 1061, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.231152 = idf(docFreq=31, maxDocs=44218)
               0.09375 = fieldNorm(doc=1061)
         0.14066313 = weight(abstract_txt:truncated in 1061) [ClassicSimilarity], result of:
           0.14066313 = score(doc=1061,freq=1.0), product of:
             0.16691889 = queryWeight, product of:
               1.2675121 = boost
               8.988837 = idf(docFreq=14, maxDocs=44218)
               0.014650412 = queryNorm
             0.84270346 = fieldWeight in 1061, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.988837 = idf(docFreq=14, maxDocs=44218)
               0.09375 = fieldNorm(doc=1061)
         0.051539652 = weight(abstract_txt:describe in 1061) [ClassicSimilarity], result of:
           0.051539652 = score(doc=1061,freq=1.0), product of:
             0.10768526 = queryWeight, product of:
               1.439768 = boost
               5.1052136 = idf(docFreq=728, maxDocs=44218)
               0.014650412 = queryNorm
             0.4786138 = fieldWeight in 1061, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.1052136 = idf(docFreq=728, maxDocs=44218)
               0.09375 = fieldNorm(doc=1061)
         0.37956846 = weight(abstract_txt:distribution in 1061) [ClassicSimilarity], result of:
           0.37956846 = score(doc=1061,freq=5.0), product of:
             0.3235281 = queryWeight, product of:
               3.9458485 = boost
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.014650412 = queryNorm
             1.1732163 = fieldWeight in 1061, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.09375 = fieldNorm(doc=1061)
       0.2 = coord(5/25)
   

3. Sarabia, J.M.; Sarabia, M.: Explicit expressions for the Leimkuhler curve in parametric families (2008) 0.15

   0.15034205 = sum of:
     0.15034205 = product of:
       0.9396378 = sum of:
         0.061391518 = weight(abstract_txt:informetric in 2120) [ClassicSimilarity], result of:
           0.061391518 = score(doc=2120,freq=1.0), product of:
             0.12584956 = queryWeight, product of:
               1.1005892 = boost
               7.805067 = idf(docFreq=48, maxDocs=44218)
               0.014650412 = queryNorm
             0.4878167 = fieldWeight in 2120, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.805067 = idf(docFreq=48, maxDocs=44218)
               0.0625 = fieldNorm(doc=2120)
         0.25647756 = weight(abstract_txt:informetrics in 2120) [ClassicSimilarity], result of:
           0.25647756 = score(doc=2120,freq=2.0), product of:
             0.37368828 = queryWeight, product of:
               3.284844 = boost
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.014650412 = queryNorm
             0.6863409 = fieldWeight in 2120, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.0625 = fieldNorm(doc=2120)
         0.2771976 = weight(abstract_txt:distribution in 2120) [ClassicSimilarity], result of:
           0.2771976 = score(doc=2120,freq=6.0), product of:
             0.3235281 = queryWeight, product of:
               3.9458485 = boost
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.014650412 = queryNorm
             0.856796 = fieldWeight in 2120, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.0625 = fieldNorm(doc=2120)
         0.34457114 = weight(abstract_txt:pareto in 2120) [ClassicSimilarity], result of:
           0.34457114 = score(doc=2120,freq=1.0), product of:
             0.5732435 = queryWeight, product of:
               4.0684557 = boost
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.014650412 = queryNorm
             0.6010904 = fieldWeight in 2120, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.0625 = fieldNorm(doc=2120)
       0.16 = coord(4/25)
   

4. Egghe, L.: Relations between the continuous and the discrete Lotka power function (2005) 0.13

   0.13335788 = sum of:
     0.13335788 = product of:
       0.8334868 = sum of:
         0.1422082 = weight(abstract_txt:continuous in 3464) [ClassicSimilarity], result of:
           0.1422082 = score(doc=3464,freq=6.0), product of:
             0.10448937 = queryWeight, product of:
               1.0028487 = boost
               7.11192 = idf(docFreq=97, maxDocs=44218)
               0.014650412 = queryNorm
             1.3609825 = fieldWeight in 3464, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               7.11192 = idf(docFreq=97, maxDocs=44218)
               0.078125 = fieldNorm(doc=3464)
         0.24090512 = weight(abstract_txt:lotka in 3464) [ClassicSimilarity], result of:
           0.24090512 = score(doc=3464,freq=6.0), product of:
             0.1484863 = queryWeight, product of:
               1.1954807 = boost
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.014650412 = queryNorm
             1.6224064 = fieldWeight in 3464, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.078125 = fieldNorm(doc=3464)
         0.12977651 = weight(abstract_txt:lotkaian in 3464) [ClassicSimilarity], result of:
           0.12977651 = score(doc=3464,freq=1.0), product of:
             0.17863649 = queryWeight, product of:
               1.3112469 = boost
               9.298992 = idf(docFreq=10, maxDocs=44218)
               0.014650412 = queryNorm
             0.72648376 = fieldWeight in 3464, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.298992 = idf(docFreq=10, maxDocs=44218)
               0.078125 = fieldNorm(doc=3464)
         0.32059693 = weight(abstract_txt:informetrics in 3464) [ClassicSimilarity], result of:
           0.32059693 = score(doc=3464,freq=2.0), product of:
             0.37368828 = queryWeight, product of:
               3.284844 = boost
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.014650412 = queryNorm
             0.85792613 = fieldWeight in 3464, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.7650614 = idf(docFreq=50, maxDocs=44218)
               0.078125 = fieldNorm(doc=3464)
       0.16 = coord(4/25)
   

5. Burrell, Q.L.: On Egghe's version of continuous concentration theory (2006) 0.12

   0.11617025 = sum of:
     0.11617025 = product of:
       0.96808547 = sum of:
         0.20097896 = weight(abstract_txt:concentration in 4903) [ClassicSimilarity], result of:
           0.20097896 = score(doc=4903,freq=3.0), product of:
             0.13247912 = queryWeight, product of:
               1.1292058 = boost
               8.008008 = idf(docFreq=39, maxDocs=44218)
               0.014650412 = queryNorm
             1.5170615 = fieldWeight in 4903, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               8.008008 = idf(docFreq=39, maxDocs=44218)
               0.109375 = fieldNorm(doc=4903)
         0.16410698 = weight(abstract_txt:truncated in 4903) [ClassicSimilarity], result of:
           0.16410698 = score(doc=4903,freq=1.0), product of:
             0.16691889 = queryWeight, product of:
               1.2675121 = boost
               8.988837 = idf(docFreq=14, maxDocs=44218)
               0.014650412 = queryNorm
             0.98315406 = fieldWeight in 4903, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.988837 = idf(docFreq=14, maxDocs=44218)
               0.109375 = fieldNorm(doc=4903)
         0.6029995 = weight(abstract_txt:pareto in 4903) [ClassicSimilarity], result of:
           0.6029995 = score(doc=4903,freq=1.0), product of:
             0.5732435 = queryWeight, product of:
               4.0684557 = boost
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.014650412 = queryNorm
             1.0519081 = fieldWeight in 4903, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.109375 = fieldNorm(doc=4903)
       0.12 = coord(3/25)