Advances and Applications in Statistics
Volume 24, Issue 2, Pages 83 - 106
(October 2011)
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THE LAMBDA DISTRIBUTION AND ITS APPLICATIONS TO CATEGORICAL SUMMARY MEASURES
Tarald O. Kv嬳eth
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Abstract: A new distribution, the lambda distribution, is introduced as a one-parameter discrete distribution of which each component is simply a weighted arithmetic mean of the corresponding components of the degenerate distribution and the rectangular (uniform) distribution This lambda distribution is (a) uniquely fit to establish necessary conditions for valid comparisons involving the numerical values of summary measures for nominal categorical data and (b) a convenient and simple means of comparing the numerical values of different summary measures, either analytically or by means of computer simulation. Such analysis is extended to ordinal categorical data by simply introducing one additional parameter to the lambda distribution. Several examples are provided, some involving established measures of variation and diversity for which difference and ratio comparisons lack validity and lead to improper and misleading results and conclusions, while some of the exemplified measures meet the validity requirements. |
Keywords and phrases: discrete distribution, categorical summary measures, valid comparisons. |
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