سعید طهماسبی

One of the main subjects of statistics, is the information theory. Nowadays the information and inaccuracy measures have a special place in reliability. In this thesis, after expressing preliminaries of inaccuracy, introduce the information measures and ordered random variables, we consider a measure of inaccuracy between distributions of the nth upper (lower) record value and parent random variable. We also express a measure of inaccuracy between distributions of the ith order statistics and parent random variable. We propose weighted cumulative past (residual) inaccuracy in record values and order statistics and we obtain a measure of inaccuracy between rth concomitant of generalized order statistic and the parent random variable in Morgenstern family. For these concepts, we obtain some properties and characterization results such as relationships with other reliability functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these measures are considered. We study on a problem of estimating the measure of inaccuracy by means of the empirical cumulative inaccuracy and weighted cumulative past (residual) inaccuracy in lower record values.