Abstract
Let X be a continuous nonnegative random variable with density f, mean µ, and finite variance σ 2. Mullooly (1988), hereafter simply Mullooly, has shown that if f is positive on the interior of its support, \(\mathop {\lim }\limits_{x \to 0} f(x) >0\frac{\sigma }{\mu } > 1\), and \(\frac{\sigma }{\mu } >1\), then σ 2 may be increased by truncation. Denote by σ 2(t), the variance of the truncated random variable X t ≡ I(t, ∞)(X), where I A is an indicator on the set A. Specifically, Mullooly demonstrates that for densities satisfying these conditions, there exists a real number T > 0 such that σ 2(t) > σ 2 for all t∈ (0,T). We shall call T the variance inflation boundary for X t . When σ 2(t) > σ 2 for all t ∈ (0, ∞), we say that T = ∞.
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© 1993 Springer Science+Business Media New York
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Bauldry, W.C., Hebert, J.L. (1993). Truncation and Variance in Scale Mixtures. In: Lee, T. (eds) Mathematical Computation with Maple V: Ideas and Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0351-3_7
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DOI: https://doi.org/10.1007/978-1-4612-0351-3_7
Publisher Name: Birkhäuser, Boston, MA
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