Characterization of the geometric distribution by the form of a predictor |
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| Authors: | SNUA Kirmani SN Alam |
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| Institution: | 1. Shiraz University , Shiraz, Iran;2. Aligarh Muslim university , Aligarh, India |
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| Abstract: | The problem of prodicting max (X1X2) given min(X1X2) is considered when Y1and Y2 are i.i.d random variables making positive integral values. It is provea tnat tne oest predictor is a linear Function or min(X1,X2); with unit slope Iff X1, and X2 have geometric distributions. As an extension of this result, the geometric distribution is characterized by the constancy of regression of min(X1?X2|, c) on inin(X1,X2) where c is any positive integer. |
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| Keywords: | order statistics constant: regression truncated ranve |
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