منابع مشابه
Some stochastic inequalities for weighted sums
We compare weighted sums of i.i.d. positive random variables according to the usual stochastic order. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Specifically, let Yi be i.i.d. random variables on R+. Assuming that log Yi has a log-concave density, we show that ∑ aiYi is stochastically smaller than ∑ biYi, if (log a1, . . . , log an) ...
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Let be a sequence of arbitrary random variables with and , for every and be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on and sequence .
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In this note, using the multisection series method, we establish the formulas for various power sums of sine or cosine functions.
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The collection of all quaternions is denoted byH and is called the real quaternionic algebra. This algebra was first introduced by Hamilton in 1843 (see [5, 6]), and is often called the Hamilton quaternionic algebra. It is well known thatH is an associative division algebra over R. For any a= a0 + a1i+ a2 j + a3k ∈H, the conjugate of a = a0 + a1i + a2 j + a3k is defined to be a = a0 − a1i− a2 j...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2001
ISSN: 1331-4343
DOI: 10.7153/mia-04-26