Thank you so much for the reply.
Yes, I meant gamma and it was my mistake. I also looked at the link which you sent me but I like to know if the procedure that I used works?
Moreover, after I fixed the spelling I received an error, regarding "n" but I am not using it inside the procedure? please see attached log file.
Thank you again
NOTE: Copyright (c) 2002-2012 by SAS Institute Inc., Cary, NC, USA.
NOTE: SAS (r) Proprietary Software 9.4 (TS1M2)
Licensed to UNIVERSITY OF JORDAN, Site 70235184.
NOTE: This session is executing on the X64_8PRO platform.
NOTE: Updated analytical products:
SAS/STAT 13.2
SAS/ETS 13.2
SAS/OR 13.2
SAS/IML 13.2
SAS/QC 13.2
NOTE: Additional host information:
X64_8PRO WIN 6.2.9200 Workstation
NOTE: SAS initialization used:
real time 0.92 seconds
cpu time 0.62 seconds
1 /*Solve system of non linear equations */
2
3 title1 'Solving a Simultaneous System';
4 data test;
5 input a b @@;
6 datalines;
NOTE: SAS went to a new line when INPUT statement reached past the end of a line.
NOTE: The data set WORK.TEST has 3 observations and 2 variables.
NOTE: DATA statement used (Total process time):
real time 0.09 seconds
cpu time 0.00 seconds
8 ;
9
NOTE: Writing HTML Body file: sashtml.htm
10 proc model data=test;
11 eq.sqrt = sqrt(x) - y;
12 eq.hyperbola = a + b / x - y;
13 solve x y / solveprint;
14 id a b;
15 run;
16
NOTE: PROCEDURE MODEL used (Total process time):
real time 28:52.50
cpu time 14.54 seconds
17 proc iml;
NOTE: IML Ready
18
19 seed=12345;
19 ! k=1;
20
21 alpha=2;
21 ! lambda=2;
22
23
24 n=100;
24 ! m=n;
24 ! R=J(m,1,0);
25
26 print alpha lambda;
27
28
29
30 W=J(m,1,0);
30 ! V=J(m,1,0);
30 ! X_p=J(m,1,0);
30 ! X_A=J(m,1,0);
30 ! U=J(m,1,0);
31
32 X=J(m,1,0);
33
34 do i=1 to m;
35 W[i]=Uniform(seed);
36 end;
37
38 S=1+R[m];
39 V[1]=W[1]**(1/S);
40
41 do i=2 to m;
42 S=S+(1+R[m-i+1]);
43 V[i]=W[i]**(1/S);
44 end;
45
46 do i=1 to m;
47
48 U[i]=1-prod( V[ m:( m-i+1)] );
48 ! ** the U's are the required progressively type II from U(0,1);
49
50 END;
51
52
53 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
54
55
56 print X;
57
58 quit;
NOTE: Exiting IML.
NOTE: PROCEDURE IML used (Total process time):
real time 0.06 seconds
cpu time 0.06 seconds
59
60 proc iml;
NOTE: IML Ready
61
62 seed=12345;
62 ! k=1;
63
64 alpha=2;
64 ! lambda=2;
65
66
67 n=10;
67 ! m=n;
67 ! R=J(m,1,0);
68
69 print alpha lambda;
70
71
72
73 W=J(m,1,0);
73 ! V=J(m,1,0);
73 ! X_p=J(m,1,0);
73 ! X_A=J(m,1,0);
73 ! U=J(m,1,0);
74
75 X=J(m,1,0);
76
77 do i=1 to m;
78 W[i]=Uniform(seed);
79 end;
80
81 S=1+R[m];
82 V[1]=W[1]**(1/S);
83
84 do i=2 to m;
85 S=S+(1+R[m-i+1]);
86 V[i]=W[i]**(1/S);
87 end;
88
89 do i=1 to m;
90
91 U[i]=1-prod( V[ m:( m-i+1)] );
91 ! ** the U's are the required progressively type II from U(0,1);
92
93 END;
94
95
96 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
97
98
99 print X;
100
101 quit;
NOTE: Exiting IML.
NOTE: PROCEDURE IML used (Total process time):
real time 0.03 seconds
cpu time 0.03 seconds
102
103 proc iml;
NOTE: IML Ready
104
105 seed=12345;
105! k=1;
106
107 alpha=2;
107! lambda=2;
108
109
110 n=10;
110! m=n;
110! R=J(m,1,0);
111
112 print alpha lambda;
113
114
115
116 W=J(m,1,0);
116! V=J(m,1,0);
116! X_p=J(m,1,0);
116! X_A=J(m,1,0);
116! U=J(m,1,0);
117
118 X=J(m,1,0);
119
120 do i=1 to m;
121 W[i]=Uniform(seed);
122 end;
123
124 S=1+R[m];
125 V[1]=W[1]**(1/S);
126
127 do i=2 to m;
128 S=S+(1+R[m-i+1]);
129 V[i]=W[i]**(1/S);
130 end;
131
132 do i=1 to m;
133
134 U[i]=1-prod( V[ m:( m-i+1)] );
134! ** the U's are the required progressively type II from U(0,1);
135
136 END;
137
138
139 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
140
141
142 *******************************************************************************;
143 *** MLE for the Kumaraswamy using Type II Adaptive progressive censoring ***** ;
144 *******************************************************************************;
145
146 start MLE_func(y) global (n,m,X,R);
147
148 func=0;
149
150 alpha=y[1];
151 lambda=y[2];
152
153
154 Sum_log=J(m,1,0);
155 Sum_log=log(x);
156
157 Sum_log_1=J(m,1,0);
158 Sum_log_1=log(1-X##lambda);
159
160
161 func=func + m*log(alpha*lambda)+(lambda-1)* Sum_log[+] + (alpha-1) * Sum_log_1[+] ;
162
163 Return(func);
164
165 finish;
NOTE: Module MLE_FUNC defined.
166
167
168
169
170 ************* Constrain MLE ***********************;
171
172 con={0.01 0.01 , . .};
173 x0={0.05, 0.05};
174 tc={10000 14000};
175
176 *************** MLE *********************;
177
178
179 call nlpnra(rc, MLE_ret, "MLE_func", x0, opt, con,tc);
ERROR: (execution) Matrix has not been set to a value.
operation : NLPNRA at line 179 column 1
operands : *LIT1049, x0, opt, con, tc
*LIT1049 1 row 1 col (character, size 😎
MLE_func
x0 2 rows 1 col (numeric)
0.05
0.05
opt 0 row 0 col (type ?, size 0)
con 2 rows 2 cols (numeric)
0.01 0.01
. .
tc 1 row 2 cols (numeric)
10000 14000
statement : CALL at line 179 column 1
180
181 alpha_mle =MLE_ret[1];
ERROR: (execution) Matrix has not been set to a value.
operation : [ at line 181 column 19
operands : MLE_ret, *LIT1050
MLE_ret 0 row 0 col (type ?, size 0)
*LIT1050 1 row 1 col (numeric)
1
statement : ASSIGN at line 181 column 1
182 lambda_mle=MLE_ret[2];
ERROR: (execution) Matrix has not been set to a value.
operation : [ at line 182 column 19
operands : MLE_ret, *LIT1051
MLE_ret 0 row 0 col (type ?, size 0)
*LIT1051 1 row 1 col (numeric)
2
statement : ASSIGN at line 182 column 1
183
184
185 print alpha_mle lambda_mle;
ERROR: Matrix alpha_mle has not been set to a value.
statement : PRINT at line 185 column 1
186
187
188
189
190 quit;
NOTE: Exiting IML.
NOTE: The SAS System stopped processing this step because of errors.
NOTE: PROCEDURE IML used (Total process time):
real time 0.08 seconds
cpu time 0.03 seconds
