= Polynomial tails prevent exponential tilting
If a density has polynomially decaying tails on both half-lines, its <moment-generating function> is infinite at every nonzero real parameter: exponential growth defeats polynomial decay on the positive tail for a positive parameter, and on the negative tail for a negative parameter. Thus no open real tilting domain exists for a <saddlepoint density approximation>, even when the distribution has finite mean and variance and a <central limit theorem> applies.
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