Pareto distribution


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Pareto distribution

the tendency for a small proportion of the number of objects or items being considered to account for a large proportion of the feature under examination. More crudely, the Pareto ‘law’ suggests that 20% of items account for 80% of the total amount of stock or sales or whatever. In the case of stock, the Pareto law implies that a small proportion of the total number of items stocked accounts for a large proportion of the total value of stock held.

The business significance of the Pareto distribution is that if management devotes the greater part of its time to controlling the most important 20% of the stock items held, it is, in effect, controlling a large proportion of the total value of the firm's stocks. See ABC ANALYSIS.

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In the appendix, we repeat the simulation analysis but modify the assumption regarding the distribution of losses such that [X.sub.1], [X.sub.2], and [X.sub.3] follow a Pareto distribution (Pareto(2, 1)).
For illustrative purposes, we assume that F takes on a simple Pareto distribution
(2014) for each sample year, to estimate the coefficient of a Type-I Pareto distribution for earnings above the 99th percentile.
Pareto's discovery has since been called many names such as Pareto Principle, Pareto Law, Pareto Distribution, Law of Least Effect, 80/rules, Principle of imbalance and 80/20 thinking (Koch, 2011a, 2011b, 2013).An expert and inordinate writer (Koch, 2011a, 2011b, 2013) in the field of Pareto Principle affirmed that the executives those who apply Pareto Principle in their duty takes enjoy more benefits or compensation whether public or private.
The thing that is interesting is that Pareto extended the 80/20 rules and developed the Pareto Distribution.
Analyzing these results, according to Figure 3, it is possible to state that the location parameter could be represented by a Generalized Pareto distribution scale parameter and the shape parameter could be represented by GEV distribution.
To determine the bilateral threshold levels and the index [V.sub.ij,t], a typical assumption is that the distribution of input requirement across firms is characterised by the Pareto distribution. If the Pareto distribution is untruncated (lower bound for the input requirement equals zero), [V.sub.ij,t] > 0 since some firms in i will have a low enough input requirement to export to j.
It should be emphasized here that many phenomena in both the natural and social sciences have power law statistics (Pareto distribution).
The simple theory of optimal taxation that Diamond and Saez provide relies on the assumption that income among the top 1 percent is distributed according to the Pareto distribution. Named after economist Vilfredo Pareto (1848-1923), it is a distribution that is known to have a thick (sometimes called a "fat") tail.
Goodness-of-fit for the generalized Pareto distribution. Technometrics, 43(4), 478-484.
Nevertheless, after reviewing the literature, the authors noted that the Pareto distribution has been gradually gaining acceptance in the modeling of sea clutter (Chakravarthi & Ozturk, 1991; Farshchian & Posner, 2010; Gelb, Heath, & Tipple, 2010; Piotrkowski, 2008; Watts & Rosenberg, 2013; G.
The Pareto distribution is a compound Gaussian model with a Rayleigh distribution being modulated by an inverse Gamma distribution [25-27].