By Barry C. Arnold
A lot of papers on Pareto distributions and comparable issues have seemed because the first version of this hadbook. This booklet updates the preferred first version by means of interleafing advancements inequality indices, parametric households of Lorenz curves, Pareto methods, hidden truncation, and more.
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Extra resources for Pareto Distributions Second Edition
Most of these authors arrived at the distribution via a mixture of exponential distributions using a gamma mixing distribution. This genesis suggests that the Pareto (II) might be well adapted to modeling reliability problems, and many of its properties are interpretable in this context. It does have Pareto-like tails and might be expected to be a viable competitor for fitting income distributions. Balkema and de Haan (1974) showed that it arises as a limit distribution of residual lifetime at great age.
Additional contributions to Lorenz curve technology included Kakwani and Podder’s (1973, 1976) suggestions of a new coordinate system and weighted least squares estimates for grouped data. , if we use a transformation g(x) with g(x)/x decreasing, then inequality will be reduced. Ord, Patil and Taillie (1981b) identified conditions under which truncation will reduce inequality. Truncation might thus cause underestimation of inequality. In a similar vein, Peterson (1979) pointed out that if Gini indices are computed using grouped data, then uniform growth of incomes (inflation) can lead to a shift in the Lorenz curve and Gini index even though the actual income distribution is unchanged in shape.
In the present monograph, to highlight its position in a hierarchy of increasingly complicated (and flexible) Pareto-like distributions, it will be called the Pareto (IV) distribution. In THE MODERN ERA 9 this hierarchy Fisk’s sech2 (or log-logistic) distribution is endowed with yet another name, Pareto (III). Hatke (1949) gave moment charts for the Burr (Pareto IV) family of distributions enabling one to compare it with the Pearson family of curves. More recent work in this area was provided by Burr and Cislak (1968), Rodriguez (1977) and Pearson, Johnson and Burr (1978).
Pareto Distributions Second Edition by Barry C. Arnold