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# Thread Subject: generate random number for certain distribution

 Subject: generate random number for certain distribution From: edward kabanyas Date: 27 May, 2008 17:16:02 Message: 1 of 10 Hi, As we know that Matlab can generate random number with several command. I need to generate random value for the following gamma distribution: f(D)=No*D^m*exp(-L*D); No, m and L will be assumed. I need to generate randomly distributed D in size of 0
 Subject: generate random number for certain distribution From: Peter Perkins Date: 27 May, 2008 17:47:27 Message: 2 of 10 edward kabanyas wrote: > As we know that Matlab can generate random number with > several command. I need to generate random value for the > following gamma distribution: jq, If you have access to the Statistics Toolbox, use the GAMRND function. If not, you may be able to find something on the MATLAB File Exchange Hope this helps. - Peter Perkins    The MathWorks, Inc.
 Subject: generate random number for certain distribution From: edward kabanyas Date: 28 May, 2008 05:35:02 Message: 3 of 10 Dear Peter; Thanks for your reply. > jq, If you have access to the Statistics Toolbox, use the GAMRND function. As you know, that gamrnd(A,B,m,n) generates gamma random numbers with parameters A and B. In my case, the gamma equation is as I sent before, contain 3 parameters (modified gamma). >If not, you may be able to find something on the MATLAB >File Exchange I try to visit the web, but I could not find the random number generator there. It is too many. Could you show me one ? Again, thanks for nice help Cheers juq
 Subject: generate random number for certain distribution From: Peter Perkins Date: 28 May, 2008 13:38:07 Message: 4 of 10 edward kabanyas wrote: > As we know that Matlab can generate random number with > several command. I need to generate random value for the > following gamma distribution: > > f(D)=No*D^m*exp(-L*D); > As you know, that gamrnd(A,B,m,n) generates gamma random > numbers with parameters A and B. In my case, the gamma > equation is as I sent before, contain 3 parameters (modified > gamma). juq, if No in your expression is anything other than L^(m+1) / gamma(m+1), you're going to have a hard time getting that "density" to integrate to 1. Your density may be written with three parameters, but only two of them are independent. Are you sure you're fitting a distribution, and not fitting a curve that just happens to have the same shape as a gamma density?
 Subject: generate random number for certain distribution From: edward kabanyas Date: 28 May, 2008 16:56:03 Message: 5 of 10 Dear Peter Perkins Thanks very much for your reply. > juq, if No in your expression is anything other than >L^(m+1) > gamma(m+1),you're going to have a hard time >getting that >"density" to integrate to 1. > f(D)=No*D^m*exp(-L*D); Actually, I do not have good knowledge in statistics. However, the mentioned modified gamma distribution is commonly used in meteorology to model raindrop or cloud drop distribution. No is intercept, L is slope and m is shape parameter. No is the same as the concept of No in the following exponential distribution: f(D) = No*exp(-L*D); I try to find the theoretical background of the above modified gammma distribution, but I can not find it. But I am sure that the above modified gamma is gamma(m+1,L). If so, is it No for gamma(m+1,L) is L^(m+1)/gamma(m+1)? If No for the above modified gamma is L^(m+1)/gamma(m+1), could we get the random value of D in interval of 0 f(D)=No*D^m*exp(-L*D); > density may be written with three parameters, but only two of them are independent. > > Are you sure you're fitting a distribution, and not fitting a curve that just > happens to have the same shape as a gamma density?
 Subject: generate random number for certain distribution From: Peter Perkins Date: 29 May, 2008 14:02:01 Message: 6 of 10 edward kabanyas wrote: > However, the mentioned modified gamma distribution is > commonly used in meteorology to model raindrop or cloud drop > distribution. No is intercept, L is slope and m is shape > parameter. No is the same as the concept of No in the > following exponential distribution: > > f(D) = No*exp(-L*D); But again, that's not an exponential density, or a density at all, unless No is equal to L. A density must integrate to 1. The above, and this: > If No for the above modified gamma is L^(m+1)/gamma(m+1), > could we get the random value of D in interval of 0 might help clear things up.
 Subject: generate random number for certain distribution From: edward kabanyas Date: 29 May, 2008 14:44:03 Message: 7 of 10 Dear Peter Perkins; Again, thanks very much for your nice discussion. I m sorry to make mistake in informing you. > sound suspiciously like you are trying to fit a curve, not >a probability distribution. Yes, you are correct. After I check some literatures, the following modified gamma distribution f(D) = No*D^m*exp(-L*D) is not probability gamma distribution but frequency distribution and the parameters No, m and L is derived from such fitting procedure. If I select certain value for No, m and L, could we get the random value of D in interval of 0 wrote in message ... > edward kabanyas wrote: > > > However, the mentioned modified gamma distribution is > > commonly used in meteorology to model raindrop or cloud drop > > distribution. No is intercept, L is slope and m is shape > > parameter. No is the same as the concept of No in the > > following exponential distribution: > > > > f(D) = No*exp(-L*D); > > But again, that's not an exponential density, or a density at all, unless No is > equal to L. A density must integrate to 1. > > The above, and this: > > > If No for the above modified gamma is L^(m+1)/gamma(m+1), > > could we get the random value of D in interval of 0 > sound suspiciously like you are trying to fit a curve, not a probability > distribution. This demo > > might help clear things up.
 Subject: generate random number for certain distribution From: Peter Perkins Date: 29 May, 2008 18:05:47 Message: 8 of 10 edward kabanyas wrote: > Yes, you are correct. After I check some literatures, the > following modified gamma distribution f(D) = > No*D^m*exp(-L*D) is not probability gamma distribution but > frequency distribution and the parameters No, m and L is > derived from such fitting procedure. A "frequency distribution" to me would mean "a probability distribution times a sample size", and it seems like you'd want No to be the sample size, and therefore your expression is _still_ missing the appropriate normalizing constant to make it integrate to 1*No. Did you look at the demo link? > If I select certain value for No, m and L, could we get the > random value of D in interval of 0 above frequency distribution? Or can not we get random value > from frequency distribution ? I still don't know what that means. If D has a gamma distribution, it is not limited to any finite range. It seems like you ought to consult with someone in your field who has more of a background in statistics.
 Subject: generate random number for certain distribution From: edward kabanyas Date: 1 Jun, 2008 15:24:01 Message: 9 of 10 Dear Peter; Thanks very much for your nice help: >I still don't know what that means. As I explained before, my modified gamma distribution (frequency distribution)is f(D)=No*D^m*exp(-L*D). (1) Probability is frequency/N (number of data). I think we can change the above (Eq. 1) to yield the density distribution: p(D)= (No*D^m*exp(-L*D))/N; how do you think ? Can we get random number from Eq. 1 if we know No, m, L and N? Again, thanks very much. Best regards; Peter Perkins wrote in message ... > edward kabanyas wrote: > > > Yes, you are correct. After I check some literatures, the > > following modified gamma distribution f(D) = > > No*D^m*exp(-L*D) is not probability gamma distribution but > > frequency distribution and the parameters No, m and L is > > derived from such fitting procedure. > > A "frequency distribution" to me would mean "a probability distribution times a > sample size", and it seems like you'd want No to be the sample size, and > therefore your expression is _still_ missing the appropriate normalizing > constant to make it integrate to 1*No. > > Did you look at the demo link? > > > > If I select certain value for No, m and L, could we get the > > random value of D in interval of 0 > above frequency distribution? Or can not we get random value > > from frequency distribution ? > > I still don't know what that means. If D has a gamma distribution, it is not > limited to any finite range. It seems like you ought to consult with someone in > your field who has more of a background in statistics.
 Subject: generate random number for certain distribution From: Peter Perkins Date: 2 Jun, 2008 13:43:32 Message: 10 of 10 edward kabanyas wrote: > Dear Peter; > > Thanks very much for your nice help: > >> I still don't know what that means. > > As I explained before, my modified gamma distribution > (frequency distribution)is > > f(D)=No*D^m*exp(-L*D). (1) > > Probability is frequency/N (number of data). > > I think we can change the above (Eq. 1) to yield the density > distribution: > > p(D)= (No*D^m*exp(-L*D))/N; > > how do you think ? Can we get random number from Eq. 1 if we > know No, m, L and N? You started out with one too many parameters; now you have two too many. I can't answer your questions. I recommend that you consult with someone in your field who has more of a statistical background.