Avaldis 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 braceti=1≤i<floorkS:Sik,i=floorkS:SlnSEk,i>floorkS:0
11
B is used to normalize the robust distribution.
12
Avaldis 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 parenthesisB=k∑i=1pi+ti
13
u is the robust distribution.
14
Avaldis 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 braceui=1≤i≤k:pi+tiB
15
Compare data points (note the change in 1 and 2, as well as the spike later on)
16
"i"i
"p" left parenthesis, "i" , right parenthesispi
"u" left parenthesis, "i" , right parenthesisui
11
r1c4:
22
r2c4:
33
r3c4:
44
r4c4:
55
r5c4:
66
r6c4:
77
r7c4:
88
r8c4:
99
r9c4:
1010
r10c4:
1111
r11c4:
1212
r12c4:
1313
r13c4:
1414
r14c4:
1515
r15c4:
1616
r16c4:
r17c4:
17
Check if distributions are normalized.
18
Avaldis 19: Start sum from "n" equals 1 to "k" , end sum, "p" left parenthesis, "n" , right parenthesisk∑n=1pn
19
Avaldis 20: Start sum from "n" equals 1 to "k" , end sum, "u" left parenthesis, "n" , right parenthesisk∑n=1un
