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The properties of the empirical density function,f n(x) = k/n(ξj + − ξj-1 +) ifξ j-1 + < x ≤ ξ+ whereξ j-1 + andξ j + are sample elements and there are exactlyk − 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a “good” estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.

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The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we first study the reliability characteristics of Morgenstern type bivariate Rayleigh distribution (MTBRD). Then, we investigate some properties on concomitants of order statistics and record values in MTBRD. Finally, we propose the best linear unbiased estimator for a parameter of MTBRD using both complete and censored samples based on concomitants of order statistics.

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