The estimators of a probability events by incomplete observations

There is considered a problem of statistical estimation of a probability of the product of twoevents on the basis of complete and incomplete observations. The estimators with using additionalinformation by incomplete observations are suggested and investigated.*0, ( ) 0,( )( )( ) 0. ( ) ( ),( )nnXYnnmnP Bn P A BP A B n m P B P A B m P Bn m P B= ⎧⎪⎪ + ⎪  = + ⎨  ⎪ + ⎪+ ⎪⎩Here Pn(A×B) and Pn(B), Pm(B) are empirical probabilities, n is a size incomplete observations,m is a size complete observations. The results are illustrated by numerical examples.There is considered a problem of statistical estimation of a probability of the product of twoevents on the basis of complete and incomplete observations. The estimators with using additionalinformation by incomplete observations are suggested and investigated.

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