I have a question regarding statistical updating. Basically I have a probability density function of a random variable X and, at each time step, I obtain a new sample $x_i$ belonging to this distribution. I know that X ~ logNormal($\mu,\sigma$). I am looking for a way to update this probability density function as a new sample $x_i$ is available a each time step. I am considering to use Bayesian analysis, but still not sure how to set-up the solution. I thank you all in advance for your hints!!! I am new in the platform and I really appreciate to start being part of it.
There is no difference between observing a normal sample $(X_1,...,X_n)$ and a log-normal sample $(Y_1,....,Y_n)$ as one can be turned into the other by a $\log$ or $\exp$ transform. You may hence use the ultra-classic Gaussian model framework (see e.g. Chapter 2 of our book!) for log-normal samples.