In practice, we often encounter situations where a sample size is not defined in advance and can be random value. The randomness of the crucially changes asymptotic properties underlying statistic. present paper second order Chebyshev--Edgeworth Cornish--Fisher expansions based Student's $t$- Laplace distributions their quantiles are derived for median with special kind.

We present a well-defined and characterized all-sky sample of classical Cepheids in the Milky Way, obtained by combining two time-domain surveys: Gaia DR2 (Gaia Collaboration et al. 2018) All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee 2014). first use parallax variability information from to select ∼30,000 bright (G < 17) Cepheid candidates with MK − 1. then analyze their ASAS-SN V-b...