How do you know which distribution to use for your problem?

[sjaguar13]

If you have a problem that involves some distribution, how do you know which one to use? The ones we covered so far are:
Binomial
Negative Binomial
Hypergeometric
Poisson Distribution
Poisson Process

 

[Haelfix]

You don't. You either take data and fit the distribution to one of those (and whichever one gives you the least error becomes the working model), or you guess the distribution from say first principles (say if you are a physicist and working on a physical problem).

 

[EnumaElish]

Sometimes you may be able to trace distributions as "precedents" or "dependents" by uisng established analytical relations between distributions. E.g., if two variables are normally distributed, then their sum is also normal, and their quotient is Cauchy. The logarithm of a Normal variable has a Log Normal distribution. And, sometimes you can approximate (distributions approach one another under certain limit conditions, so it may be possible to use a simpler distribution in place of a more complex one).

 

[EnumaElish]

And at some level, you do know. For example, you know whether it's a discrete or a continuous distribution. Also, we know that centain types of "experiments" are associated with certain distributions. Thus, a coin toss is associated with binomial; "consumer choice" is associated with multinomial; the number of balls in each of N boxes is associated with Chi-square; the number of customers arriving "between 9AM and 10AM" is associated wtih Poisson.