Details

Autor(en) / Beteiligte

• Balakrishnan, Narayanaswamy
• Rychtář, Jan
• Taylor, Dewey
• Walter, Stephen D.

Titel

Accurate approximation of the expected value, standard deviation, and probability density function of extreme order statistics from Gaussian samples

Ist Teil von

• Communications in statistics. Simulation and computation, 2024-02, Vol.53 (2), p.869-878

Ort / Verlag

Philadelphia: Taylor & Francis

Erscheinungsjahr

2024

Quelle

Taylor & Francis

Beschreibungen/Notizen

• We show that the expected value of the largest order statistic in Gaussian samples can be accurately approximated as ( 0.2069   ln   ( ln   ( n ) ) + 0.942 ) 4 , where n ∈ [ 2 , 10 8 ] is the sample size, while the standard deviation of the largest order statistic can be approximated as − 0.4205 arctan ( 0.5556 [ ln ( ln   ( n ) ) − 0.9148 ] ) + 0.5675 . We also provide an approximation of the probability density function of the largest order statistic which in turn can be used to approximate its higher order moments. The proposed approximations are computationally efficient, and improve previous approximations of the mean and standard deviation given by Chen and Tyler ( 1999 ).