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In practice, we often encounter situations where a sample size is not definedin advance and can be a random value. The randomness of the sample sizecrucially changes the asymptotic properties of the underlying statistic. In thepresent paper second order Chebyshev--Edgeworth and Cornish--Fisher expansionsbased of Student's $t$- and Laplace distributions and their quantiles arederived for sample median with random sample size of a special kind.

Second Order Expansions for Sample Median with Random Sample Size