Thank you so much for your efforts. i really appreciate it.  My integration is the product of three quantities 1-standard normal pdf "normal" 2- a scaled chi distribution with degrees of freedom "df" 3- The quantity (v*avrl) which is a function of both variables QQ and ZED where ZED is the variable following the standard normal distribution and QQ is the variable following a scaled chi distribution. The inner module is used to compute the quantity "v*avrl".  After computing the quantitty "v*avrl" which depends on both ZED and QQ, the inner integrand is computed by multipying "v*avrl" by the normal density. The result of the inner integration should be a function of QQ which is called "w" in our syntax. This w is multiplied by the scaled chi distribution: (1/cf)*(1/sqrt(df))*(2**(1-(df/2)))*(QQ**(df-1))*(exp((-QQ**2)/2))/gamma(df/2); Thus, i think I have to call QUAD for both the inner and outer integrals since "v*avrl" depends on both QQ and ZED, see this part in the syntax: QQstar1=(QQ*z[i, ])+(ZED/(sqrt(mm))); QQstar=QQstar1-shift; kone=QQstar+QQ*fun1; ktwo=QQstar+QQ*fun2; pij=probnorm(kone)-probnorm(ktwo); Thus "v*avrl"is not a constant with respect to the inner integral. Am I correct?? Aya ... View more

The plots are attached. Each plot is for a certain QQ value (1,3,5) and different ZED values(-5,-4,-3,-2,-1,0,1,2,3,4,5). I have made many trials to have this integration done, but I am always faced with errors. Sometimes related to the singularity of a matrix, so i tried the " ginv"  function, so I got errors related to the convergence of the integral over the specified interval. I really can't figure out what the problem is. I tried running the syntax for other integration limits; ZEDinterval (-1,1) and Qinterval (0,1), It gave me an answer  without errors " 1.659E-59". The correct answer over the whole interval (-inf,inf) and(0,inf) is supposed to be 339.4!! Aya    ... View more

I am sorry that I am asking too many questions concerning this code.But it is really very important in my research.   I have been trying to correct the errors concerning the singularity of a matrix, so i used ginv function to avoid these errors. However, I got other errors related to Convergence could not be attained over the subinterval              ( 0 , .P) Convergence could not be attained over the subinterval              ( .M , .P) Could you please help me to point out the reasons behind these errors? Waiting for your reply, Aya      ... View more

Thanks alot Rick. The inner function was returning a vector of values. I corrected this mistake, However I got other errors. I don't know how could I overcome these errors. I think this time it is related to the singularity of a matrix!! The modified program is attached. ... View more

I run my model once again and it took 10 minutes to get the output i attached before, my questions are: 1-does the output indicate problems in the model?does the output indicate that my constraint is violated or that the optimal parameter estimates won't result in the displayed optimal objective value? 2-why the optimal parameter estimates don't satisfy the constraints and don't result in the optimal objective value? 3-why every time i run my model i get different answers? 4-Does this part of the output indicate that the constraint is satisfied? if so, why when i substitute with the optimal values in my constraint, i find that the constraint is not satisfied?                        Values of Nonlinear Constraints                                                                                                                                              Constraint          Residual                                                                                                                                                        [            1 ]           0 Active  NLEC Waiting for your reply, Emara ... View more

Thanks alot for ur help, I attached the syntax containing my model. I tried to run the syntax without the consraint as you mentioned and i got the following output: Optimization Start Active Constraints                            0  Objective Function                  3.469302357 　                                                         Objective     Std Dev  Restart                   Function       Active      Objective   Function  of Simplex   Vertex  Simplex Iter   Restarts     Calls  Constraints       Function     Change      Values   Length     Size     1          0        20            2        3.45151     0.0125     0.00540    1.000    0.200                                       Optimization Results Iterations                                    1  Function Calls                               22 Restarts                                      0  Active Constraints                            2 Objective Function                 3.4657027053  Std Dev of Simplex Values          0.0053965381 Deltax                                        1  Size                                     0.1995 All parameters are actively constrained.  Optimization cannot proceed. NOTE: At least one element of the (projected) gradient is greater than 1e-3. Optimization Start Active Constraints                            0  Objective Function                  3.469302357 　                                                         Objective     Std Dev  Restart                   Function       Active      Objective   Function  of Simplex   Vertex  Simplex Iter   Restarts     Calls  Constraints       Function     Change      Values   Length     Size     1          0        20            2        3.45151     0.0125     0.00540    1.000    0.200                                       Optimization Results Iterations                                    1  Function Calls                               22 Restarts                                      0  Active Constraints                            2 Objective Function                 3.4657027053  Std Dev of Simplex Values          0.0053965381 Deltax                                        1  Size                                     0.1995 All parameters are actively constrained.  Optimization cannot proceed. NOTE: At least one element of the (projected) gradient is greater than 1e-3. Optimization Results                                        Parameter Estimates                                                            Active                                                            Bound                            N Parameter         Estimate    Constraint                            1 X1                       0     Lower BC                            2 X2                1.000000     Upper BC                            Value of Objective Function = 3.4657027053 　 The Lagrange multipliers for active lower bounds are equal to the corresponding gradient     element; for upper bounds, they are equal to the negative gradient element. Tthanks, Emara ... View more

Here is the paper "Optimization designs of the combined Shewhart-CUSUM control charts" Waiting for your reply, Emara ... View more

Dear Dr. Rick, I dont understand exactly what is wrong, could u clarify more if possible. I will try to clarify more what I am doing. The idea is like  minimizing type two error(qq module in my syntax) ,fixing type one error (qq0 in my syntax) at a certain level for a hypothesis test in which the null hypothesis is that diff=0 versus the alternative hypothesis diff not=0 (diff is the integration variable in my syntax). However, in my program, I want to minimize "qq" over the whole range of the variable "diff" (0,0.5). That is why I am integrating qq over the variable diff as if I am obtaining an expected value of qq. I want to keep "type one error" at a certain level (100 in my syntax). Thus my objective function is "OBJ" and my non linear constraint is "qq0=100". Type one error and two errors in my syntax dont have a closed formula to be computed and are both computed using simulation (100 runs in my syntax). My aim is to find the values of hr[1] and hr[2] that gives me the minimum type two error , fixing type one error at  certain level (of course what is written in my syntax is not type one and two errors, but the idea is similar). Can't I do this using SAS? Please let me know if this is not possible using SAS or if I cant clarify what i am doing. I know that the minimization problem can be solved as it is done in several papers, but i want to solve it using SAS Thank u for ur help, Emara ... View more