The continuous random variable with uniform point inequality measure
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By using the conditions that the expected value of an absolute random variable X is finite and positive
and that the point inequality measure I ðpÞ is uniform for 0 < p < 1, this paper discusses the
question of the existence of such random variable and proves that this problem has a unique solution.
The obtained cumulative distribution function of X is a truncated Pareto distribution, with traditional
inequality parameter equal to 0,5 and with support depending on the finite and positive expected
value and the level of uniformity, based on the ratios between the lower means and the
upper means, used for defining the point inequality measure I(p).
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