In the context of additive or multiplicative damage models, and under mild conditions, it is shown that the functional forms of suitably chosen regressions on a random variable X or/and its recorded part Y are charact...
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In the context of additive or multiplicative damage models, and under mild conditions, it is shown that the functional forms of suitably chosen regressions on a random variable X or/and its recorded part Y are characteristic of the distribution of X. The paper treats the cases where the recorded value is either an understatement or an overstatement of the true observation.
In this note, we assume that the reported income is related to the true income by the so-called ‘error-in-variables’ model, a model which assumes that the observed incomes are under-reported. In the context of this ...
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In this note, we assume that the reported income is related to the true income by the so-called ‘error-in-variables’ model, a model which assumes that the observed incomes are under-reported. In the context of this model, the distribution of the reported income suitably truncated below coincides with that of the true income, and suitable truncated above with that of the random proportion of the reported income to the true income if, and only if, the distribution of the true income is Pareto and that of the proportion is of the powerfunction form.
Suppose that in a random sample of size n from a population with probability density function f(x) , the order statistics are X (1) < X (2) < … < X (n) . It is proved that a necessary and sufficient conditio...
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Suppose that in a random sample of size n from a population with probability density function f(x) , the order statistics are X (1) < X (2) < … < X (n) . It is proved that a necessary and sufficient condition for f(x) to be the density function of the power function distribution is that the statistics X (r)/X (s) and X (t) (1 ≤ r < s < t ≤ n) are independent.
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