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Table 1 Approximation errors for C(k,n : F) systems

From: Approximating the distributions of runs and patterns

n

k

q

Exact

FMCI

Poisson

CP

5

2

0.01

0.99960

0.00000

-0.00010

0.00000

5

2

0.10

0.96309

0.00000

-0.00788

0.00119

5

2

0.25

0.79980

-0.00002

-0.02697

0.04654

10

2

0.01

0.99911

0.00000

-0.00010

0.00000

10

2

0.10

0.91975

0.00000

-0.00728

0.00312

10

2

0.25

0.61180

0.00000

-0.00869

0.12266

10

4

0.01

1.00000

0.00000

0.00000

0.00000

10

4

0.10

0.99936

0.00000

-0.00026

0.00000

10

4

0.25

0.97855

0.00000

-0.00776

0.00038

50

2

0.01

0.99516

0.00000

-0.00010

0.00000

50

2

0.10

0.63633

0.00000

-0.00251

0.01871

50

2

0.25

0.07173

0.00000

0.14441

0.96838

50

4

0.01

1.00000

0.00000

0.00000

0.00000

50

4

0.10

0.99577

0.00000

-0.00026

0.00000

50

4

0.25

0.86897

0.00000

-0.00663

0.00312

100

2

0.01

0.99024

0.00000

-0.00010

0.00000

100

2

0.10

0.40151

0.00000

0.00343

0.03854

100

2

0.25

0.00492

0.00000

0.36933

2.97133

100

4

0.01

1.00000

0.00000

0.00000

0.00000

100

4

0.10

0.99129

0.00000

-0.00026

0.00001

100

4

0.25

0.74908

0.00000

-0.00523

0.00656

500

4

0.20

0.52721

0.00000

-0.00086

0.00611

1,000

4

0.20

0.27696

0.00000

0.00183

0.01232

10,000

5

0.20

0.07710

0.00000

0.00183

0.00560