Soliton Distributions

t is added to p to form the robust distribution.

Uttryck 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.

Uttryck 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

u is the robust distribution.

Uttryck 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			r1c4:
2			r2c4:
3			r3c4:
4			r4c4:
5			r5c4:
6			r6c4:
7			r7c4:
8			r8c4:
9			r9c4:
10			r10c4:
11			r11c4:
12			r12c4:
13			r13c4:
14			r14c4:
15			r15c4:
16			r16c4:
			r17c4:

Check if distributions are normalized.

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

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

driven av