Document (#33062)

Author
Shan, S.
Title
On the generalized Zipf distribution : part I
Source
Information processing and management. 41(2005) no.6, S.1369-1386
Year
2005
Abstract
This article is concerned with a class of informetric distribution, a family of skew distributions found to describe a wide range of phenomena both within or outside of information sciences and referred to as being of Zipf-type. A generalization of Zipf distribution (a size-frequency form of the Zipf's law), named the generalized Zipf distribution, is introduced. Two main characterizations of the generalized Zipf distribution are obtained based on the proportionate hazard rate and truncated moments. Finally, some asymptotic properties of the generalized Zipf distribution are investigated.
Footnote
Beitrag in einem "Special Issue on Infometrics"
Theme
Informetrie
Object
Zipf-Verteilung

Similar documents (content)

  1. Burrell, Q.L.: Extending Lotkaian informetrics (2008) 0.26
    0.26380032 = sum of:
      0.26380032 = product of:
        0.73277867 = sum of:
          0.027054872 = weight(abstract_txt:properties in 3126) [ClassicSimilarity], result of:
            0.027054872 = score(doc=3126,freq=1.0), product of:
              0.058910772 = queryWeight, product of:
                1.0290443 = boost
                5.878422 = idf(docFreq=337, maxDocs=44421)
                0.009738676 = queryNorm
              0.4592517 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.878422 = idf(docFreq=337, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.03409607 = weight(abstract_txt:outside in 3126) [ClassicSimilarity], result of:
            0.03409607 = score(doc=3126,freq=1.0), product of:
              0.06873331 = queryWeight, product of:
                1.1115278 = boost
                6.3496094 = idf(docFreq=210, maxDocs=44421)
                0.009738676 = queryNorm
              0.49606323 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                6.3496094 = idf(docFreq=210, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.034483865 = weight(abstract_txt:phenomena in 3126) [ClassicSimilarity], result of:
            0.034483865 = score(doc=3126,freq=1.0), product of:
              0.06925349 = queryWeight, product of:
                1.1157259 = boost
                6.3735914 = idf(docFreq=205, maxDocs=44421)
                0.009738676 = queryNorm
              0.49793684 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                6.3735914 = idf(docFreq=205, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.04236563 = weight(abstract_txt:distributions in 3126) [ClassicSimilarity], result of:
            0.04236563 = score(doc=3126,freq=1.0), product of:
              0.07944017 = queryWeight, product of:
                1.1949694 = boost
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.009738676 = queryNorm
              0.53330237 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.04680991 = weight(abstract_txt:referred in 3126) [ClassicSimilarity], result of:
            0.04680991 = score(doc=3126,freq=1.0), product of:
              0.08490298 = queryWeight, product of:
                1.2353731 = boost
                7.057077 = idf(docFreq=103, maxDocs=44421)
                0.009738676 = queryNorm
              0.55133414 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                7.057077 = idf(docFreq=103, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.06343917 = weight(abstract_txt:informetric in 3126) [ClassicSimilarity], result of:
            0.06343917 = score(doc=3126,freq=1.0), product of:
              0.103976704 = queryWeight, product of:
                1.367114 = boost
                7.809647 = idf(docFreq=48, maxDocs=44421)
                0.009738676 = queryNorm
              0.6101287 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                7.809647 = idf(docFreq=48, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.07439948 = weight(abstract_txt:generalization in 3126) [ClassicSimilarity], result of:
            0.07439948 = score(doc=3126,freq=1.0), product of:
              0.11563189 = queryWeight, product of:
                1.441702 = boost
                8.235732 = idf(docFreq=31, maxDocs=44421)
                0.009738676 = queryNorm
              0.6434166 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                8.235732 = idf(docFreq=31, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.096880764 = weight(abstract_txt:truncated in 3126) [ClassicSimilarity], result of:
            0.096880764 = score(doc=3126,freq=1.0), product of:
              0.13788682 = queryWeight, product of:
                1.5743383 = boost
                8.993418 = idf(docFreq=14, maxDocs=44421)
                0.009738676 = queryNorm
              0.70261073 = fieldWeight in 3126, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                8.993418 = idf(docFreq=14, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
          0.31324896 = weight(abstract_txt:distribution in 3126) [ClassicSimilarity], result of:
            0.31324896 = score(doc=3126,freq=5.0), product of:
              0.32039413 = queryWeight, product of:
                5.878339 = boost
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.009738676 = queryNorm
              0.9776988 = fieldWeight in 3126, product of:
                2.236068 = tf(freq=5.0), with freq of:
                  5.0 = termFreq=5.0
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.078125 = fieldNorm(doc=3126)
        0.36 = coord(9/25)
    
  2. Ye, F.Y.: ¬A theoretical approach to the unification of informetric models by wave-heat equations (2011) 0.23
    0.23159352 = sum of:
      0.23159352 = product of:
        1.1579676 = sum of:
          0.03816564 = weight(abstract_txt:size in 464) [ClassicSimilarity], result of:
            0.03816564 = score(doc=464,freq=1.0), product of:
              0.059209865 = queryWeight, product of:
                1.0316532 = boost
                5.8933253 = idf(docFreq=332, maxDocs=44421)
                0.009738676 = queryNorm
              0.64458245 = fieldWeight in 464, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.8933253 = idf(docFreq=332, maxDocs=44421)
                0.109375 = fieldNorm(doc=464)
          0.08387967 = weight(abstract_txt:distributions in 464) [ClassicSimilarity], result of:
            0.08387967 = score(doc=464,freq=2.0), product of:
              0.07944017 = queryWeight, product of:
                1.1949694 = boost
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.009738676 = queryNorm
              1.0558848 = fieldWeight in 464, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.109375 = fieldNorm(doc=464)
          0.12560314 = weight(abstract_txt:informetric in 464) [ClassicSimilarity], result of:
            0.12560314 = score(doc=464,freq=2.0), product of:
              0.103976704 = queryWeight, product of:
                1.367114 = boost
                7.809647 = idf(docFreq=48, maxDocs=44421)
                0.009738676 = queryNorm
              1.2079931 = fieldWeight in 464, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                7.809647 = idf(docFreq=48, maxDocs=44421)
                0.109375 = fieldNorm(doc=464)
          0.19612485 = weight(abstract_txt:distribution in 464) [ClassicSimilarity], result of:
            0.19612485 = score(doc=464,freq=1.0), product of:
              0.32039413 = queryWeight, product of:
                5.878339 = boost
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.009738676 = queryNorm
              0.61213624 = fieldWeight in 464, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.109375 = fieldNorm(doc=464)
          0.71419424 = weight(abstract_txt:zipf in 464) [ClassicSimilarity], result of:
            0.71419424 = score(doc=464,freq=1.0), product of:
              0.758357 = queryWeight, product of:
                9.043763 = boost
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.009738676 = queryNorm
              0.94176525 = fieldWeight in 464, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.109375 = fieldNorm(doc=464)
        0.2 = coord(5/25)
    
  3. Egghe, L.; Guns, R.: Applications of the generalized law of Benford to informetric data (2012) 0.18
    0.17983097 = sum of:
      0.17983097 = product of:
        1.1239436 = sum of:
          0.07439948 = weight(abstract_txt:generalization in 1376) [ClassicSimilarity], result of:
            0.07439948 = score(doc=1376,freq=1.0), product of:
              0.11563189 = queryWeight, product of:
                1.441702 = boost
                8.235732 = idf(docFreq=31, maxDocs=44421)
                0.009738676 = queryNorm
              0.6434166 = fieldWeight in 1376, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                8.235732 = idf(docFreq=31, maxDocs=44421)
                0.078125 = fieldNorm(doc=1376)
          0.18800974 = weight(abstract_txt:generalized in 1376) [ClassicSimilarity], result of:
            0.18800974 = score(doc=1376,freq=1.0), product of:
              0.34054247 = queryWeight, product of:
                4.948258 = boost
                7.0667386 = idf(docFreq=102, maxDocs=44421)
                0.009738676 = queryNorm
              0.552089 = fieldWeight in 1376, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                7.0667386 = idf(docFreq=102, maxDocs=44421)
                0.078125 = fieldNorm(doc=1376)
          0.14008918 = weight(abstract_txt:distribution in 1376) [ClassicSimilarity], result of:
            0.14008918 = score(doc=1376,freq=1.0), product of:
              0.32039413 = queryWeight, product of:
                5.878339 = boost
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.009738676 = queryNorm
              0.43724018 = fieldWeight in 1376, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.078125 = fieldNorm(doc=1376)
          0.72144514 = weight(abstract_txt:zipf in 1376) [ClassicSimilarity], result of:
            0.72144514 = score(doc=1376,freq=2.0), product of:
              0.758357 = queryWeight, product of:
                9.043763 = boost
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.009738676 = queryNorm
              0.95132655 = fieldWeight in 1376, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.078125 = fieldNorm(doc=1376)
        0.16 = coord(4/25)
    
  4. Arsenault, C.: Aggregation consistency and frequency of Chinese words and characters (2006) 0.17
    0.17032243 = sum of:
      0.17032243 = product of:
        0.85161215 = sum of:
          0.044863395 = weight(abstract_txt:frequency in 734) [ClassicSimilarity], result of:
            0.044863395 = score(doc=734,freq=4.0), product of:
              0.060331736 = queryWeight, product of:
                1.0413809 = boost
                5.948895 = idf(docFreq=314, maxDocs=44421)
                0.009738676 = queryNorm
              0.7436119 = fieldWeight in 734, product of:
                2.0 = tf(freq=4.0), with freq of:
                  4.0 = termFreq=4.0
                5.948895 = idf(docFreq=314, maxDocs=44421)
                0.0625 = fieldNorm(doc=734)
          0.08301934 = weight(abstract_txt:distributions in 734) [ClassicSimilarity], result of:
            0.08301934 = score(doc=734,freq=6.0), product of:
              0.07944017 = queryWeight, product of:
                1.1949694 = boost
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.009738676 = queryNorm
              1.0450549 = fieldWeight in 734, product of:
                2.4494898 = tf(freq=6.0), with freq of:
                  6.0 = termFreq=6.0
                6.82627 = idf(docFreq=130, maxDocs=44421)
                0.0625 = fieldNorm(doc=734)
          0.09147572 = weight(abstract_txt:zipf's in 734) [ClassicSimilarity], result of:
            0.09147572 = score(doc=734,freq=1.0), product of:
              0.15399559 = queryWeight, product of:
                1.6637605 = boost
                9.504243 = idf(docFreq=8, maxDocs=44421)
                0.009738676 = queryNorm
              0.5940152 = fieldWeight in 734, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                9.504243 = idf(docFreq=8, maxDocs=44421)
                0.0625 = fieldNorm(doc=734)
          0.2241427 = weight(abstract_txt:distribution in 734) [ClassicSimilarity], result of:
            0.2241427 = score(doc=734,freq=4.0), product of:
              0.32039413 = queryWeight, product of:
                5.878339 = boost
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.009738676 = 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)
          0.408111 = weight(abstract_txt:zipf in 734) [ClassicSimilarity], result of:
            0.408111 = score(doc=734,freq=1.0), product of:
              0.758357 = queryWeight, product of:
                9.043763 = boost
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.009738676 = queryNorm
              0.53815156 = fieldWeight in 734, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.0625 = fieldNorm(doc=734)
        0.2 = coord(5/25)
    
  5. Ding, C.H.Q.: ¬A probabilistic model for Latent Semantic Indexing (2005) 0.16
    0.16271271 = sum of:
      0.16271271 = product of:
        1.0169544 = sum of:
          0.024828091 = weight(abstract_txt:introduced in 4459) [ClassicSimilarity], result of:
            0.024828091 = score(doc=4459,freq=1.0), product of:
              0.05563225 = queryWeight, product of:
                5.7125063 = idf(docFreq=398, maxDocs=44421)
                0.009738676 = queryNorm
              0.44628954 = fieldWeight in 4459, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.7125063 = idf(docFreq=398, maxDocs=44421)
                0.078125 = fieldNorm(doc=4459)
          0.028039621 = weight(abstract_txt:frequency in 4459) [ClassicSimilarity], result of:
            0.028039621 = score(doc=4459,freq=1.0), product of:
              0.060331736 = queryWeight, product of:
                1.0413809 = boost
                5.948895 = idf(docFreq=314, maxDocs=44421)
                0.009738676 = queryNorm
              0.4647574 = fieldWeight in 4459, product of:
                1.0 = tf(freq=1.0), with freq of:
                  1.0 = termFreq=1.0
                5.948895 = idf(docFreq=314, maxDocs=44421)
                0.078125 = fieldNorm(doc=4459)
          0.2426416 = weight(abstract_txt:distribution in 4459) [ClassicSimilarity], result of:
            0.2426416 = score(doc=4459,freq=3.0), product of:
              0.32039413 = queryWeight, product of:
                5.878339 = boost
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.009738676 = queryNorm
              0.75732225 = fieldWeight in 4459, product of:
                1.7320508 = tf(freq=3.0), with freq of:
                  3.0 = termFreq=3.0
                5.5966744 = idf(docFreq=447, maxDocs=44421)
                0.078125 = fieldNorm(doc=4459)
          0.72144514 = weight(abstract_txt:zipf in 4459) [ClassicSimilarity], result of:
            0.72144514 = score(doc=4459,freq=2.0), product of:
              0.758357 = queryWeight, product of:
                9.043763 = boost
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.009738676 = queryNorm
              0.95132655 = fieldWeight in 4459, product of:
                1.4142135 = tf(freq=2.0), with freq of:
                  2.0 = termFreq=2.0
                8.610425 = idf(docFreq=21, maxDocs=44421)
                0.078125 = fieldNorm(doc=4459)
        0.16 = coord(4/25)