Research Article

Computing the Moments of Order Statistics from Independent Nonidentically Distributed Exponentiated Frechet Variables

Table 2

𝐼 𝑗 ( 𝑘 ) using (3.5) when 𝑛 = 3 .

j 𝐼 𝑗 ( 𝑘 )

1 𝐼 1 ( 𝑘 ) = 𝑘 𝜎 𝑘 Γ ( ( 𝑘 / 𝜆 ) ) 𝜆 𝑛 𝑖 = 1 𝛼 𝑖 𝑚 = 0 ( 𝛼 𝑖 𝑚 ) ( 1 ) 𝛼 𝑖 𝑚 ( 𝛼 𝑖 𝑚 ) 𝑘 / 𝜆
2 𝐼 2 ( 𝑘 ) = 𝑘 𝜎 𝑘 Γ ( 𝑘 / 𝜆 ) 𝜆 𝛼 1 + 𝛼 2 𝑚 = 0 𝛼 1 + 𝛼 2 𝑚 ( 1 ) 𝛼 1 + 𝛼 2 𝑚 ( 𝛼 1 + 𝛼 2 𝑚 ) 𝑘 / 𝜆
+ 𝛼 1 + 𝛼 3 𝑚 = 0 𝛼 1 + 𝛼 3 𝑚 ( 1 ) 𝛼 1 + 𝛼 3 𝑚 ( 𝛼 1 + 𝛼 3 𝑚 ) 𝑘 / 𝜆
+ 𝛼 2 + 𝛼 3 𝑚 = 0 𝛼 2 + 𝛼 3 𝑚 ( 1 ) 𝛼 2 + 𝛼 3 𝑚 ( 𝛼 2 + 𝛼 3 𝑚 ) 𝑘 / 𝜆
3 𝑘 𝜎 𝑘 Γ ( 𝑘 / 𝜆 ) 𝜆 𝛼 1 + 𝛼 2 + 𝛼 3 𝑚 = 0 𝛼 1 + 𝛼 2 + 𝛼 3 𝑚 ( 1 ) 𝛼 1 + 𝛼 2 + 𝛼 3 𝑚 ( 𝛼 1 + 𝛼 2 + 𝛼 3 𝑚 ) 𝑘 / 𝜆