Computing lognormal parameter using maximum likelihood method

Can anyone please tell me how can I calculate lognormal parameter of a function using maximum likelihood method for a given set of data.

I have attached two file in which fragility is on y-axis and velocity is one x-axis. This data follow log normal distribution having function

f(a)=(log(velocity(i)/median))/standard_deviation

F = ((f(a)^fragility(i))*((1.0-f(a))^(1.0-fragility(i)))); This F should undergo maximum likelihood method to compute standard deviation and median values through an iterative procedure?

It would be better if someone help me using a code so that I can understand well?