Order Statistics

Order Statistics

The order statistic procedure computes the distribution of the rth sample drawn from the random variable X, given a sample size of n, where n >= r.

Syntax

OrderStat(X,n,r)

Examples:

In [3]: X=TriangularRV(Rational(1),Rational(5),Rational(9))

In [4]: Y=OrderStat(X,5,2)

In [5]: Y.display()
continuous pdf
for 1 <= x <= 5
---------------------------
                           3               
          ⎛   2           ⎞  ⎛ 2          ⎞
5⋅(x - 1)⋅⎝- x  + 2⋅x + 31⎠ ⋅⎝x  - 2⋅x + 1⎠
───────────────────────────────────────────
                  4194304                  
---------------------------
 
 
for 5 <= x <= 9
---------------------------
                                           3
          ⎛ 2            ⎞ ⎛ 2            ⎞ 
5⋅(x - 9)⋅⎝x  - 18⋅x + 49⎠⋅⎝x  - 18⋅x + 81⎠ 
────────────────────────────────────────────
                  4194304                   
---------------------------