Document (#28466)

Author
Egghe, L.
Title
Relations between the continuous and the discrete Lotka power function
Source
Journal of the American Society for Information Science and Technology. 56(2005) no.7, S.664-668
Year
2005
Abstract
The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, ... items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.
Theme
Informetrie
Object
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. Egghe, L.; Rousseau, R.: ¬The Hirsch index of a shifted Lotka function and its relation with the impact factor (2012) 0.21
    0.21319051 = sum of:
      0.21319051 = product of:
        1.0659525 = sum of:
          0.023106532 = weight(abstract_txt:number in 2244) [ClassicSimilarity], result of:
            0.023106532 = score(doc=2244,freq=2.0), product of:
              0.042245403 = queryWeight, product of:
                1.0867895 = boost
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.0094224755 = queryNorm
              0.5469597 = fieldWeight in 2244, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.09375 = fieldNorm(doc=2244)
          0.025227567 = weight(abstract_txt:sources in 2244) [ClassicSimilarity], result of:
            0.025227567 = score(doc=2244,freq=1.0), product of:
              0.056435175 = queryWeight, product of:
                1.2561185 = boost
                4.7681975 = idf(docFreq=976, maxDocs=42306)
                0.0094224755 = queryNorm
              0.4470185 = fieldWeight in 2244, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                4.7681975 = idf(docFreq=976, maxDocs=42306)
                0.09375 = fieldNorm(doc=2244)
          0.040473394 = weight(abstract_txt:items in 2244) [ClassicSimilarity], result of:
            0.040473394 = score(doc=2244,freq=1.0), product of:
              0.07734152 = queryWeight, product of:
                1.4704899 = boost
                5.5819464 = idf(docFreq=432, maxDocs=42306)
                0.0094224755 = queryNorm
              0.52330744 = fieldWeight in 2244, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.5819464 = idf(docFreq=432, maxDocs=42306)
                0.09375 = fieldNorm(doc=2244)
          0.28616282 = weight(abstract_txt:function in 2244) [ClassicSimilarity], result of:
            0.28616282 = score(doc=2244,freq=4.0), product of:
              0.27250707 = queryWeight, product of:
                5.1639094 = boost
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0094224755 = queryNorm
              1.0501115 = fieldWeight in 2244, product of:
                2.0 = tf(freq=4.0), with freq of:
                  4.0 = termFreq=4.0
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.09375 = fieldNorm(doc=2244)
          0.6909822 = weight(abstract_txt:lotka in 2244) [ClassicSimilarity], result of:
            0.6909822 = score(doc=2244,freq=2.0), product of:
              0.6179551 = queryWeight, product of:
                7.776213 = boost
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.0094224755 = queryNorm
              1.1181755 = fieldWeight in 2244, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.09375 = fieldNorm(doc=2244)
        0.2 = coord(5/25)
    
  2. Burrell, Q.L.: Formulae for the h-index : a lack of robustness in Lotkaian informetrics? (2013) 0.20
    0.19741797 = sum of:
      0.19741797 = product of:
        0.8225749 = sum of:
          0.017638875 = weight(abstract_txt:model in 2978) [ClassicSimilarity], result of:
            0.017638875 = score(doc=2978,freq=3.0), product of:
              0.040392492 = queryWeight, product of:
                1.0626886 = boost
                4.0339417 = idf(docFreq=2035, maxDocs=42306)
                0.0094224755 = queryNorm
              0.436687 = fieldWeight in 2978, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                4.0339417 = idf(docFreq=2035, maxDocs=42306)
                0.0625 = fieldNorm(doc=2978)
          0.0119215725 = weight(abstract_txt:important in 2978) [ClassicSimilarity], result of:
            0.0119215725 = score(doc=2978,freq=1.0), product of:
              0.044865876 = queryWeight, product of:
                1.119989 = boost
                4.251453 = idf(docFreq=1637, maxDocs=42306)
                0.0094224755 = queryNorm
              0.2657158 = fieldWeight in 2978, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                4.251453 = idf(docFreq=1637, maxDocs=42306)
                0.0625 = fieldNorm(doc=2978)
          0.061488096 = weight(abstract_txt:lotkaian in 2978) [ClassicSimilarity], result of:
            0.061488096 = score(doc=2978,freq=1.0), product of:
              0.106302746 = queryWeight, product of:
                1.2190259 = boost
                9.254789 = idf(docFreq=10, maxDocs=42306)
                0.0094224755 = queryNorm
              0.57842433 = fieldWeight in 2978, 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=2978)
          0.07195411 = weight(abstract_txt:informetrics in 2978) [ClassicSimilarity], result of:
            0.07195411 = score(doc=2978,freq=1.0), product of:
              0.14872964 = queryWeight, product of:
                2.0391748 = boost
                7.740661 = idf(docFreq=49, maxDocs=42306)
                0.0094224755 = queryNorm
              0.48379132 = fieldWeight in 2978, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                7.740661 = idf(docFreq=49, maxDocs=42306)
                0.0625 = fieldNorm(doc=2978)
          0.09538761 = weight(abstract_txt:function in 2978) [ClassicSimilarity], result of:
            0.09538761 = score(doc=2978,freq=1.0), product of:
              0.27250707 = queryWeight, product of:
                5.1639094 = boost
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0094224755 = queryNorm
              0.3500372 = fieldWeight in 2978, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0625 = fieldNorm(doc=2978)
          0.56418467 = weight(abstract_txt:lotka in 2978) [ClassicSimilarity], result of:
            0.56418467 = score(doc=2978,freq=3.0), product of:
              0.6179551 = queryWeight, product of:
                7.776213 = boost
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.0094224755 = queryNorm
              0.9129865 = fieldWeight in 2978, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.0625 = fieldNorm(doc=2978)
        0.24 = coord(6/25)
    
  3. Egghe, L.: ¬A model for the size-frequency function of coauthor pairs (2008) 0.17
    0.17401104 = sum of:
      0.17401104 = product of:
        0.8700552 = sum of:
          0.012729762 = weight(abstract_txt:model in 186) [ClassicSimilarity], result of:
            0.012729762 = score(doc=186,freq=1.0), product of:
              0.040392492 = queryWeight, product of:
                1.0626886 = boost
                4.0339417 = idf(docFreq=2035, maxDocs=42306)
                0.0094224755 = queryNorm
              0.3151517 = fieldWeight in 186, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                4.0339417 = idf(docFreq=2035, maxDocs=42306)
                0.078125 = fieldNorm(doc=186)
          0.036023635 = weight(abstract_txt:number in 186) [ClassicSimilarity], result of:
            0.036023635 = score(doc=186,freq=7.0), product of:
              0.042245403 = queryWeight, product of:
                1.0867895 = boost
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.0094224755 = queryNorm
              0.8527232 = fieldWeight in 186, product of:
                2.6457512 = tf(freq=7.0), with freq of:
                  7.0 = termFreq=7.0
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.078125 = fieldNorm(doc=186)
          0.07686012 = weight(abstract_txt:lotkaian in 186) [ClassicSimilarity], result of:
            0.07686012 = score(doc=186,freq=1.0), product of:
              0.106302746 = queryWeight, product of:
                1.2190259 = boost
                9.254789 = idf(docFreq=10, maxDocs=42306)
                0.0094224755 = queryNorm
              0.72303045 = fieldWeight in 186, 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=186)
          0.16862306 = weight(abstract_txt:function in 186) [ClassicSimilarity], result of:
            0.16862306 = score(doc=186,freq=2.0), product of:
              0.27250707 = queryWeight, product of:
                5.1639094 = boost
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0094224755 = queryNorm
              0.6187842 = fieldWeight in 186, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.078125 = fieldNorm(doc=186)
          0.5758186 = weight(abstract_txt:lotka in 186) [ClassicSimilarity], result of:
            0.5758186 = score(doc=186,freq=2.0), product of:
              0.6179551 = queryWeight, product of:
                7.776213 = boost
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.0094224755 = queryNorm
              0.931813 = fieldWeight in 186, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.078125 = fieldNorm(doc=186)
        0.2 = coord(5/25)
    
  4. Egghe, L.: Type/Token-Taken informetrics (2003) 0.17
    0.17400783 = sum of:
      0.17400783 = product of:
        0.5437745 = sum of:
          0.015404355 = weight(abstract_txt:number in 2609) [ClassicSimilarity], result of:
            0.015404355 = score(doc=2609,freq=2.0), product of:
              0.042245403 = queryWeight, product of:
                1.0867895 = boost
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.0094224755 = queryNorm
              0.3646398 = fieldWeight in 2609, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                4.125428 = idf(docFreq=1857, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.061488096 = weight(abstract_txt:lotkaian in 2609) [ClassicSimilarity], result of:
            0.061488096 = score(doc=2609,freq=1.0), product of:
              0.106302746 = queryWeight, product of:
                1.2190259 = boost
                9.254789 = idf(docFreq=10, maxDocs=42306)
                0.0094224755 = queryNorm
              0.57842433 = fieldWeight in 2609, 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=2609)
          0.016818378 = weight(abstract_txt:sources in 2609) [ClassicSimilarity], result of:
            0.016818378 = score(doc=2609,freq=1.0), product of:
              0.056435175 = queryWeight, product of:
                1.2561185 = boost
                4.7681975 = idf(docFreq=976, maxDocs=42306)
                0.0094224755 = queryNorm
              0.29801235 = fieldWeight in 2609, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                4.7681975 = idf(docFreq=976, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.04673465 = weight(abstract_txt:items in 2609) [ClassicSimilarity], result of:
            0.04673465 = score(doc=2609,freq=3.0), product of:
              0.07734152 = queryWeight, product of:
                1.4704899 = boost
                5.5819464 = idf(docFreq=432, maxDocs=42306)
                0.0094224755 = queryNorm
              0.6042634 = fieldWeight in 2609, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                5.5819464 = idf(docFreq=432, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.00960035 = weight(abstract_txt:from in 2609) [ClassicSimilarity], result of:
            0.00960035 = score(doc=2609,freq=2.0), product of:
              0.03883457 = queryWeight, product of:
                1.4736011 = boost
                2.796878 = idf(docFreq=7014, maxDocs=42306)
                0.0094224755 = queryNorm
              0.24721143 = fieldWeight in 2609, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                2.796878 = idf(docFreq=7014, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.07080218 = weight(abstract_txt:item in 2609) [ClassicSimilarity], result of:
            0.07080218 = score(doc=2609,freq=3.0), product of:
              0.1020198 = queryWeight, product of:
                1.6888766 = boost
                6.4109373 = idf(docFreq=188, maxDocs=42306)
                0.0094224755 = queryNorm
              0.6940043 = fieldWeight in 2609, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                6.4109373 = idf(docFreq=188, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.22753888 = weight(abstract_txt:informetrics in 2609) [ClassicSimilarity], result of:
            0.22753888 = score(doc=2609,freq=10.0), product of:
              0.14872964 = queryWeight, product of:
                2.0391748 = boost
                7.740661 = idf(docFreq=49, maxDocs=42306)
                0.0094224755 = queryNorm
              1.5298826 = fieldWeight in 2609, product of:
                3.1622777 = tf(freq=10.0), with freq of:
                  10.0 = termFreq=10.0
                7.740661 = idf(docFreq=49, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
          0.09538761 = weight(abstract_txt:function in 2609) [ClassicSimilarity], result of:
            0.09538761 = score(doc=2609,freq=1.0), product of:
              0.27250707 = queryWeight, product of:
                5.1639094 = boost
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0094224755 = queryNorm
              0.3500372 = fieldWeight in 2609, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.600595 = idf(docFreq=424, maxDocs=42306)
                0.0625 = fieldNorm(doc=2609)
        0.32 = coord(8/25)
    
  5. Egghe, L.: Zipfian and Lotkaian continuous concentration theory (2005) 0.17
    0.17337129 = sum of:
      0.17337129 = product of:
        1.0835706 = sum of:
          0.014901966 = weight(abstract_txt:important in 4679) [ClassicSimilarity], result of:
            0.014901966 = score(doc=4679,freq=1.0), product of:
              0.044865876 = queryWeight, product of:
                1.119989 = boost
                4.251453 = idf(docFreq=1637, maxDocs=42306)
                0.0094224755 = queryNorm
              0.33214477 = fieldWeight in 4679, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                4.251453 = idf(docFreq=1637, maxDocs=42306)
                0.078125 = fieldNorm(doc=4679)
          0.113877736 = weight(abstract_txt:power in 4679) [ClassicSimilarity], result of:
            0.113877736 = score(doc=4679,freq=4.0), product of:
              0.12552303 = queryWeight, product of:
                2.2943678 = boost
                5.8062453 = idf(docFreq=345, maxDocs=42306)
                0.0094224755 = queryNorm
              0.90722585 = fieldWeight in 4679, product of:
                2.0 = tf(freq=4.0), with freq of:
                  4.0 = termFreq=4.0
                5.8062453 = idf(docFreq=345, maxDocs=42306)
                0.078125 = fieldNorm(doc=4679)
          0.24955997 = weight(abstract_txt:continuous in 4679) [ClassicSimilarity], result of:
            0.24955997 = score(doc=4679,freq=1.0), product of:
              0.44588864 = queryWeight, product of:
                6.605458 = boost
                7.1640477 = idf(docFreq=88, maxDocs=42306)
                0.0094224755 = queryNorm
              0.55969125 = fieldWeight in 4679, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                7.1640477 = idf(docFreq=88, maxDocs=42306)
                0.078125 = fieldNorm(doc=4679)
          0.7052309 = weight(abstract_txt:lotka in 4679) [ClassicSimilarity], result of:
            0.7052309 = score(doc=4679,freq=3.0), product of:
              0.6179551 = queryWeight, product of:
                7.776213 = boost
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.0094224755 = queryNorm
              1.1412332 = fieldWeight in 4679, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                8.433808 = idf(docFreq=24, maxDocs=42306)
                0.078125 = fieldNorm(doc=4679)
        0.16 = coord(4/25)