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- W4367676819 abstract "Concise and convenient bounds are obtained for the probability mass and cumulative distribution functions associated with the first success run of length <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a sequence of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Bernoulli trials. Results are compared to an approximation obtained by the Stein–Chen method as well as to bounds obtained from statistical reliability theory. These approximation formulas are used to obtain precise estimates of the expectation value associated with the occurrence of at least one success run of length <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> within <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper N> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=application/x-tex>N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> concurrent sequences of Bernoulli trials." @default.
- W4367676819 created "2023-05-03" @default.
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- W4367676819 date "2023-05-02" @default.
- W4367676819 modified "2023-10-18" @default.
- W4367676819 title "Approximations for success run probabilities in Bernoulli trials" @default.
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- W4367676819 doi "https://doi.org/10.1090/tpms/1186" @default.
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