ρ

ρ , β

ε ~ N ( 0 , 0.5 2 )

ε ~ U [ 3 2 , 3 2 ]

ε ~ 1 8 χ 2 ( 8 ) 1

Mean

SD

Mean

SD

Mean

SD

Rook

−0.9

ρ

−0.9002

0.0055

−0.8994

0.0061

−0.8994

0.0060

β

2.9996

0.0230

3.0006

0.0220

3.0005

0.0226

−0.5

ρ

−0.5000

0.0125

−0.4996

0.0121

−0.5003

0.0128

β

2.9983

0.0259

2.9994

0.0250

2.9987

0.0274

−0.1

ρ

−0.0997

0.0124

−0.1005

0.0118

−0.1007

0.0125

β

2.9994

0.0316

3.0011

0.0310

3.0015

0.0284

0

ρ

−0.0013

0.0125

−0.0004

0.0120

0.0003

0.0123

β

3.0008

0.0312

3.0008

0.0311

2.9979

0.0328

0.1

ρ

0.0992

0.0113

0.1004

0.0112

0.1000

0.0112

β

3.0018

0.0337

2.9992

0.0331

2.9989

0.0338

0.5

ρ

0.5003

0.0072

0.5005

0.0069

0.4999

0.0070

β

3.0007

0.0372

2.9962

0.0348

3.0010

0.0361

0.9

ρ

0.9002

0.0015

0.9001

0.0016

0.9002

0.0014

β

2.9961

0.0370

2.9967

0.0390

2.9958

0.0381

Queen

−0.9

ρ

−0.8990

0.0178

−0.8994

0.0061

−0.8994

0.0060

β

2.9985

0.0280

3.0006

0.0220

3.0005

0.0226

−0.5

ρ

−0.4997

0.0167

−0.4996

0.0121

−0.5003

0.0128

β

2.9979

0.0298

2.9994

0.0250

2.9987

0.0274

−0.1

ρ

−0.0998

0.0141

−0.1005

0.0118

−0.1007

0.0125

β

2.9995

0.0343

3.0011

0.0310

3.0015

0.0284

0

ρ

−0.0010

0.0131

−0.0004

0.0120

0.0003

0.0123

β

3.0004

0.0327

3.0008

0.0311

2.9979

0.0328

0.1

ρ

0.0988

0.0118

0.1004

0.0112

0.1000

0.0112

β

3.0028

0.0346

2.9992

0.0331

2.9989

0.0338

0.5

ρ

0.5004

0.0071

0.5005

0.0069

0.4999

0.0070

β

3.0001

0.0366

2.9962

0.0348

3.0010

0.0361

0.9

ρ

0.9002

0.0014

0.9001

0.0016

0.9002

0.0014

β

2.9971

0.0367

2.9967

0.0390

2.9958

0.0381