I have a series of data which pretty much follow a log normal distribution. I want to take the mle to extract the first two moments; however, the distribution is truncated. That is, my data starts at 1 not at 0. I have been using the dfittool of matlab but I am just not able to truncate my distribution at 1. Any guess?Thank you,Alan

i don't think you can fit it properly when the half of your distribution is gone.

Meaning we absolutely have to start from zero? I have a series which starts at 1 and finish at 7000. Instead of doing the MLE starting from zero i want to start from 1 therefore, I do not remove any observations. The dfittool of matlab always start at zero under a lognormal distribution and consequently the two parameters to be estimated are wrong.

QuoteOriginally posted by: Alan696Meaning we absolutely have to start from zero? I have a series which starts at 1 and finish at 7000. Instead of doing the MLE starting from zero i want to start from 1 therefore, I do not remove any observations. The dfittool of matlab always start at zero under a lognormal distribution and consequently the two parameters to be estimated are wrong.can you post the functional form of your intended distribution?what i was concerned was that it seemed from your description that you'd be fitting the distribution to the data which represents only one half of your domain: 0 to infinity. maybe you meant something else by "starts from 1".

Characteristics of the density and cumulative functions of the log-normal distribution: f(x;mu,sig)=1/(x*sig*sqrt(2*n))*e^((-z^2/2) ), x>0 F(x;mu,sig)= F(z) ,where : z=(log(x)-mu)/sigThen, I should build the conditional log-normal, x0 is the threshold 1 and x are always larger than x0.f(x; mu,sig|x > or equal to x0 )=(f(x; mu,sig))/(1-F(x0; mu,sig)) pour x > or equal to x0 ,f(x; mu,sig|x > or equal to x0 )=(F(x; mu,sig)-F(x0;mu,sig))/(1-F(x0; mu,sig)) for x> or equal to x0 .Afterwards, I should estimate the parameters with the MLE :L(x_i; mu,sig)= SUM (i=1) to n (Log(f(xi; mu,sig))-nLog(1-F(x0; mu,sig) ).How can I perform this test in matlab using these specifications?

Thank you guys, your help is very much appreciated.