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Jensen’s difference without probability vectors and actuarial applications |
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PP: 276-300 |
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Author(s) |
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Athanasios Sachlas,
Takis Papaioannou,
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Abstract |
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| In mathematics and statistics there exist many divergences. One of them, which has
a special appeal since it originates from Shannon’s entropy (a well known index of
diversity) and its concavity property, is Jensen’s difference as it was called by Burbea
and Rao [9]. Continuing our research on the properties and the use of divergence and
information measures in the actuarial field, in the present paper, we investigate the
properties of the Jensen difference in the case of non-probability vectors. This appears
in actuarial graduation. Jensen’s difference without probability vectors is an appropriate
divergence if the vectors have equal element totals. We also investigate the use of
Jensen’s difference in the problem of determining a client’s disability distribution [6]. |
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