Generalized Gaussians satisfy X_p =^d V X_q with positive V independent of X_q if and only if p ≤ q, with explicit V constructed from α-stable laws and size-biasing when p < q.
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New conditions are given for when a distribution is uniquely determined by its sequence of q-moments, together with comparisons to classical moment determinacy.
New results establish moment-indeterminacy properties of the power Lindley distribution for certain parameter ranges and demonstrate its use on software metrics data.
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Stable size-biasing and the positive scale-mixture order of generalized Gaussian laws
Generalized Gaussians satisfy X_p =^d V X_q with positive V independent of X_q if and only if p ≤ q, with explicit V constructed from α-stable laws and size-biasing when p < q.
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On the q-moment determinacy of probability distributions
New conditions are given for when a distribution is uniquely determined by its sequence of q-moments, together with comparisons to classical moment determinacy.