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Randomized geometric analysis demonstrates transitions of q-parameters in escort distributions, implying new insights into divergence measures.
From an information geometric perspective, this study considers a natural foliation of dualistic structures associated with escort distributions of exponential families. We propose an extended divergence on this foliation by continuous-type escort distributions. Specifically, we investigate the foliation formed by escort distributions to analyze the transition of q-parameters, rather than relying on a fixed parameter. Within this foliation, distinct q-parameters and their corresponding dualistic α-parameters were defined on each leaf. Finally, we present a decomposition of the extended divergence on this foliation, providing an analog to the method previously established for discrete escort distributions.
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Keiko Uohashi (2026) studied this question.
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