*J. Japan Statist. Soc.,* Vol. 31 (No. 2), pp. 257-267, 2001

## A Higher Order Large-Deviation Approximation for the Discrete Distributions

Masafumi Akahira and Kunihiko Takahashi

**Abstract. **
For a sum of independent discrete random variables, its higher order large-deviation approximation is discussed. An approximation to the tail probability of the distribution of the sum is provided, and its numerical comparison with other approximations is done in the binomial case. Consequently, the approximation formula is seen to be more accurate.

*Key words and phrases*:
Large-deviation approximation; Edgeworth expansion; Saddlepoint approximation; Binomial distribution.

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