Soliton Distributions

t is added to p to form the robust distribution.

Вираз 11: "t" left parenthesis, "i" , right parenthesis equals left brace, 1 less than or equal to "i" less than floor left parenthesis, StartFraction, "k" Over "S" , EndFraction , right parenthesis : StartFraction, "S" Over "i" "k" , EndFraction , "i" equals floor left parenthesis, StartFraction, "k" Over "S" , EndFraction , right parenthesis : StartFraction, "S" ln left parenthesis, StartNestedFraction, "S" NestedOver "E" , EndNestedFraction , right parenthesis Over "k" , EndFraction , "i" greater than floor left parenthesis, StartFraction, "k" Over "S" , EndFraction , right parenthesis : 0 , right brace

B is used to normalize the robust distribution.

Вираз 13: "B" equals Start sum from "i" equals 1 to "k" , end sum, left parenthesis, "p" left parenthesis, "i" , right parenthesis plus "t" left parenthesis, "i" , right parenthesis , right parenthesis

equals

1.4 2 8 9 6 9 5 2 6 4 8

u is the robust distribution.

Вираз 15: "u" left parenthesis, "i" , right parenthesis equals left brace, 1 less than or equal to "i" less than or equal to "k" : StartFraction, left parenthesis, "p" left parenthesis, "i" , right parenthesis plus "t" left parenthesis, "i" , right parenthesis , right parenthesis Over "B" , EndFraction , right brace

Compare data points (note the change in 1 and 2, as well as the spike later on)

"i"	"p" left parenthesis, "i" , right parenthesis	"u" left parenthesis, "i" , right parenthesis
1	r1c2: 0.0 6 2 5	r1c3: 0.1 1 9 5 2 9 6 6	r1c4:
2	r2c2: 0.5	r2c3: 0.3 8 7 7 9 8 4 2	r2c4:
3	r3c2: 0.1 6 6 6 6 6 6 7	r3c3: 0.1 4 1 8 9 8 1 2	r3c4:
4	r4c2: 0.0 8 3 3 3 3 3 3 3	r4c3: 0.0 7 7 2 6 5 0 4 5	r4c4:
5	r5c2: 0.0 5	r5c3: 0.0 5 0 1 4 8 6 2	r5c4:
6	r6c2: 0.0 3 3 3 3 3 3 3 3	r6c3: 0.0 3 5 9 5 8 8 0 8	r6c4:
7	r7c2: 0.0 2 3 8 0 9 5 2 4	r7c3: 0.0 2 7 4 8 9 4 3 1	r7c4:
8	r8c2: 0.0 1 7 8 5 7 1 4 3	r8c3: 0.0 2 1 9 7 0 4 9 9	r8c4:
9	r9c2: 0.0 1 3 8 8 8 8 8 9	r9c3: 0.1 0 3 9 2 3 1	r9c4:
10	r10c2: 0.0 1 1 1 1 1 1 1 1	r10c3: 0.0 0 7 7 7 5 6 1 1	r10c4:
11	r11c2: 0.0 0 9 0 9 0 9 0 9 1	r11c3: 0.0 0 6 3 6 1 8 6 3 5	r11c4:
12	r12c2: 0.0 0 7 5 7 5 7 5 7 6	r12c3: 0.0 0 5 3 0 1 5 5 2 9	r12c4:
13	r13c2: 0.0 0 6 4 1 0 2 5 6 4	r13c3: 0.0 0 4 4 8 5 9 2 9 4	r13c4:
14	r14c2: 0.0 0 5 4 9 4 5 0 5 5	r14c3: 0.0 0 3 8 4 5 0 8 2 3	r14c4:
15	r15c2: 0.0 0 4 7 6 1 9 0 4 8	r15c3: 0.0 0 3 3 3 2 4 0 4 7	r15c4:
16	r16c2: 0.0 0 4 1 6 6 6 6 6 7	r16c3: 0.0 0 2 9 1 5 8 5 4 1	r16c4:
	r17c2:	r17c3:	r17c4:

Check if distributions are normalized.

Вираз 19: Start sum from "n" equals 1 to "k" , end sum, "p" left parenthesis, "n" , right parenthesis

equals

Вираз 20: Start sum from "n" equals 1 to "k" , end sum, "u" left parenthesis, "n" , right parenthesis

equals

за підтримки