-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathConstructPDF.m
182 lines (160 loc) · 6.26 KB
/
ConstructPDF.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
%% Construct PDF
%
% First version: Richard Tol, 2 November 2011
% This version: Richard Tol, 29 March 2021
%display('Construct joint PDF');
global M
global V
SCCmin = -500;
SCCgrid(1)= SCCmin;
NGrid = 8111; %7601 is the maximum
for i=1:NGrid-1
SCCgrid(i+1)=SCCgrid(i)+1;
end
SCCmax = SCCgrid(end);
if JohnsonSU
gridamp = 50;
SCCtgrid(1) = asinh(SCCmin);
SCCtstep = (asinh(SCCmax) - asinh(SCCmin))/(gridamp*NGrid-1);
for i=1:gridamp*NGrid-1
SCCtgrid(i+1) = SCCtgrid(i) + SCCtstep;
end
vkernel = zeros(gridamp*NGrid,NEstimates);
%figure
j = 1;
SCCt = asinh(SCC);
SampleAve = sum(SCCt(Filter(:,j)).*TotalWeight(Filter(:,j)))/sum(TotalWeight(Filter(:,j)));
vAveSq = sum(SCCt(Filter(:,j)).*SCCt(Filter(:,j)).*TotalWeight(Filter(:,j)))/sum(TotalWeight(Filter(:,j)));
SampleStDev = sqrt(vAveSq-SampleAve*SampleAve);
V = SampleStDev^2;
for i=1:NEstimates,
mu = SCCt(i);
if Silverman
sig = 1.06*SampleStDev(j)/NEstimates^0.2;
else
sig = SampleStDev(j);
end
vkernel(:,i) = exp(-0.5*(SCCtgrid-mu).^2/sig/sig)/sig/sqrt(2*pi);
end
vkernel(isnan(vkernel)) = 0;
scale = sum(vkernel);
for i=1:NEstimates,
if scale(i)>0
vkernel(:,i) = vkernel(:,i)/scale(i);
end
end
Weight(:,j) = Filter(:,j).*TotalWeight;
PDFt = vkernel*Weight(:,j);
vsum = sum(PDFt);
PDFt = PDFt/vsum;
%plot(SCCtgrid,PDFt)
vgrid = sinh(SCCtgrid);
jacob = (1 + vgrid.*(vgrid.*vgrid+1).^-0.5)./(vgrid + (vgrid.*vgrid+1).^0.5); %note: divide and multiply by SCCtgrid
PDFtt = PDFt./jacob';
for i=1:NGrid
JointCDF(i,j) = sum(PDFtt(SCCtgrid<asinh(SCCgrid(i))));
end
JointPDF(1,j) = JointCDF(1,j);
for i=2:NGrid
JointPDF(i,j) = JointCDF(i,j) - JointCDF(i-1,j);
end
JointPDF(:,j) = JointPDF(:,j)/sum(JointPDF(:,j));
else
clear vkernel
for j=1:NFilter,
%display(j)
SampleAverage(j) = sum(SCC(Filter(:,j)).*TotalWeight(Filter(:,j)))/sum(TotalWeight(Filter(:,j)));
vAveSq = sum(SCC(Filter(:,j)).*SCC(Filter(:,j)).*TotalWeight(Filter(:,j)))/sum(TotalWeight(Filter(:,j)));
SampleStDev(j) = sqrt(vAveSq-SampleAverage(j)*SampleAverage(j));
V = SampleStDev(j)^2;
for i=1:NEstimates,
if nosplit
mu = SCC(i);
if Silverman
sig = 1.06*SampleStDev(j)/NEstimates^0.2;
else
sig = SampleStDev(j);
end
vkernel(:,i) = exp(-0.5*(SCCgrid-mu).^2/sig/sig)/sig/sqrt(2*pi);
else
if Neg(i)==0
switch distpos
case 'normal'
mu = SCC(i);
if Silverman
sig = 1.06*SampleStDev(j)/NEstimates^0.2;
else
sig = SampleStDev(j);
end
vkernel(502:NGrid,i) = exp(-0.5*(SCCgrid(502:NGrid)-mu).^2/sig/sig)/sig/sqrt(2*pi);
case 'gamma'
alpha = (SCC(i)/SampleStDev(j))^2; %mean
beta = SCC(i)/SampleStDev(j)^2;
vkernel(502:NGrid,i) = beta^alpha / gamma(alpha) * exp(-beta*SCCgrid(502:NGrid)) .* SCCgrid(502:NGrid).^(alpha-1);
case 'lognormal'
sig = log((SampleStDev(j)/SCC(i))^2+1);
mu = log(SCC(i)) - 0.5*sig;
vkernel(502:NGrid,i) = exp(-0.5*((log(SCCgrid(502:NGrid))-mu)).^2/sig)./SCCgrid(502:NGrid)/sqrt(2*sig*pi);
case 'gumbel'
mu = SCC(i); %mode
%sig = SampleStDev(j)*sqrt(6)/sqrt(pi);
sig = SampleStDev(j)*sqrt(6)/pi;
%mu = SCC(i) - sig*0.5772; %mean
vkernel(502:NGrid,i) = exp(-(SCCgrid(502:NGrid)-mu)/sig).*exp(-exp(-(SCCgrid(502:NGrid)-mu)/sig))/sig;
otherwise %Weibull
if SCC(i) == 0
kappa = 1;
lambda = SampleStDev(j)/sqrt(gamma(3)-gamma(2)^2);
else
M = SCC(i);
kappa = fminbnd(@varWeib,1,10000); %find kappa by minimizing squared distance between sample and population variance
lambda = SampleStDev(j)/sqrt(gamma(1+2/kappa)-gamma(1+1/kappa)^2);
%lambda = M * (kappa/(kappa-1))^(2/kappa); %this leads to a much wider distribution
%lambda = SampleStDev(j)/sqrt(gamma(1+2/kappa)-gamma(1+1/kappa)^2)/gamma(1+1/kappa);
end
vkernel(502:NGrid,i) = (kappa/lambda) * (SCCgrid(502:NGrid)/lambda).^(kappa-1) .* exp(-(SCCgrid(502:NGrid)/lambda).^kappa);
end
else
switch distneg
case 'normal'
mu = SCC(i);
if Silverman
sig = 1.06*SampleStDev(j)/NEstimates^0.2;
else
sig = SampleStDev(j);
end
vkernel(:,i) = exp(-0.5*(SCCgrid-mu).^2/sig/sig)/sig/sqrt(2*pi);
otherwise %Gumbel
mu = SCC(i);
%sig = SampleStDev(j)*sqrt(6)/sqrt(pi);
sig = SampleStDev(j)*sqrt(6)/pi;
vkernel(:,i) = exp(-(SCCgrid-mu)/sig).*exp(-exp(-(SCCgrid-mu)/sig))/sig;
end
end
end
end
vkernel(isnan(vkernel)) = 0;
scale = sum(vkernel);
for i=1:NEstimates,
if scale(i)>0
vkernel(:,i) = vkernel(:,i)/scale(i);
end
end
Weight(:,j) = Filter(:,j).*TotalWeight;
JointPDF(:,j) = vkernel*Weight(:,j);
vsum = sum(JointPDF(:,j));
JointPDF(:,j) = JointPDF(:,j)/vsum;
if j == 1 %store results for decomposition
allkernel = vkernel;
end
%subplot(NFilter,1,j)
%plot(SCCgrid,JointPDF(:,j))
%title(Titles{j})
end
end
JointCDF=zeros(NGrid,NFilter);
JointCDF(1,:)=JointPDF(1,:);
for i=2:NGrid,
JointCDF(i,:)=JointCDF(i-1,:)+JointPDF(i,:);
end
%clear v*