I want to keep track of $12$ financial instruments each of which updates independently from the others. There is a calculation that I want to perform that involves all $12$ numbers so every time an instrument updates I will need to recalculate my metric.
With no real good reason, I am going to assume that the logarithm of the time between updates will approximate a normal distribution - Is there a better assumption I could make prior to gathering any data?
Then given $12$ normal distributions, how can I calculate how frequently I need to recalculate my metric for it to stay up to date?
Thanks in advance.
A simpler assumption may be that the time between updates of each individual instrument has an exponential distribution, i.e. is a Poisson process.
If the twelve updating processes are independent, then the time between updates of any of them would also be exponentially distributed, and happen at a rate (the reciprocal of the expected time) which is the sum of the rates of the individual processes.