A Comparative Study of Data Transformations for Wavelet Shrinkage Estimation with Application to Software Reliability Assessment

Table 1

Representative data transformaions.

	Data transformation	Inverse data transformation	Distribution of random variable after DT
BT1 [18]	𝐵𝑖=2𝑌𝑖	𝑌𝑖=1/4×{(𝐵𝑖)^2}	𝑁(2𝜆𝑖−1/4,1)
BT2 [18]	𝐵𝑖=2𝑌𝑖+1/2	𝑌𝑖=1/4×{(𝐵𝑖)^2−2}	𝑁(2𝜆𝑖+1/4,1)
AT [16]	𝑆𝑖=2𝑌𝑖+3/8	𝑌𝑖=1/4×{(𝑆𝑖)^2−3/2}	𝑁(2𝜆𝑖+1/8,1)
FT [19]	𝐹𝑖=𝑌𝑖+1+𝑌𝑖	𝑌𝑖=1/4×{(𝐹𝑖)^2+(𝐹𝑖)^−2−2}	𝑁(2𝜆𝑖,1)