On the mean past lifetime of records

In the present paper, we consider the mean past lifetime (MPLR) of record values from a sequence of identically independent random variables with a common continuous distribution F. Under the condition that (n+1)st shock has arrived by time t > 0, we obtain a simplified expression for the mean past lifetime of the (m+1)st shock. We investigate some monotonicity properties, aging properties and characterizations for themean past lifetime of records. It is proved that the underlying distributionF can be recovered via the functional relationship between the mean past lifetime of records. Some examples are also provided.