On asymptotic behavior of some record functions
نویسندگان
چکیده
The range and midrange are widely used, particularly in statistical quality control as an estimator of the dispersion tendency. In fact, the range itself is a very simple measure of dispersion, gives a quick and easy to estimate indication about the spread of data. The extremal quotient is used in climatic study, industrial quality control, life testing, small-area variation analysis and the classical heterogeneity of variance situation. In this paper, sufficient conditions for the weak convergence of the record range, record midrange, record extremal quotient and record extremal product are obtained. The classes of non-degenerate limit distribution functions of these statistics are characterized. Illustrative examples are provided, which lend further support to our theoretical results.
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