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19 papers · 1 filter
Monotonicity properties of the Poisson approximation to the binomial distribution
Iosif Pinelis
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate…
Positive-part moments via the characteristic functions, and more general expressions
Iosif Pinelis
A unifying and generalizing approach to representations of the positive-part and absolute moments and of a random variable for real in…
Exact upper and lower bounds on the difference between the arithmetic and geometric means
Iosif Pinelis
Let denote a nonnegative random variable with . Upper and lower bounds on are obtained, which are exact, in terms of $V_…
An optimal three-way stable and monotonic spectrum of bounds on quantiles: a spectrum of coherent measures of financial risk and economic inequality
Iosif Pinelis
A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible expon…
Characteristic function of the positive part of a random variable and related results, with applications
Iosif Pinelis
Let be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) . Integral expressions for the c.f.\ of the r.v.'s in terms of $f…
Exact Rosenthal-type inequalities for p=3, and related results
Iosif Pinelis
An exact Rosenthal-type inequality for the third absolute moments is given, as well as a number of related results. Such results are useful in applications to Berry--Esseen bounds.