Studentized range distribution

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CDF

F R ( q ; k , ν ) = 2 π k ν ν / 2 Γ ( ν / 2 ) 2 ( ν / 2 − 1 ) ∫ 0 ∞ s ν − 1 φ ( ν s ) × [ ∫ − ∞ ∞ φ ( z ) [ Φ ( z + q s ) − Φ ( z ) ] k − 1 d z ] d s {\displaystyle {\begin{matr…

Parameters

k > 1, the number of groups ν {\displaystyle \nu } > 0, the degrees of freedom

PDF

f R ( q ; k , ν ) = 2 π k ( k − 1 ) ν ν / 2 Γ ( ν / 2 ) 2 ( ν / 2 − 1 ) ∫ 0 ∞ s ν φ ( ν s ) × [ ∫ − ∞ ∞ φ ( z + q s ) φ ( z ) [ Φ ( z + q s ) − Φ ( z ) ] k − 2 d z ] d s {\displ…

Support

q ∈ ( 0 , + ∞ ) {\displaystyle q\in (0,+\infty )}