The Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.
Properties for generalized cumulative past measures of information / Calì, Camilla; Longobardi, Maria; Navarro, Jorge. - In: PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES. - ISSN 0269-9648. - 34:1(2020), pp. 92-111. [10.1017/S0269964818000360]
Properties for generalized cumulative past measures of information
Calì, Camilla;Longobardi, Maria;
2020
Abstract
The Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.File | Dimensione | Formato | |
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