Point estimates for probability moments

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  • Emilio Rosenblueth
    Instituto de Ingenieria, Universidad Nacional Autónoma de México, México 20, D.F., Mexico

説明

<jats:p> Given a well-behaved real function <jats:italic>Y</jats:italic> of a real random variable <jats:italic>X</jats:italic> and the first two or three moments of <jats:italic>X</jats:italic> , expressions are derived for the moments of <jats:italic>Y</jats:italic> as linear combinations of powers of the point estimates <jats:italic> y(x <jats:sub>+</jats:sub> ) </jats:italic> and <jats:italic> y(x <jats:sub>-</jats:sub> ) </jats:italic> , where <jats:italic>x</jats:italic> <jats:sub>+</jats:sub> and <jats:italic>x</jats:italic> <jats:sub>-</jats:sub> are specific values of <jats:italic>X</jats:italic> . Higher-order approximations and approximations for discontinuous <jats:italic>Y</jats:italic> using more point estimates are also given. Second-moment approximations are generalized to the case when <jats:italic>Y</jats:italic> is a function of several variables. </jats:p>

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