Thread: Types of distributions and when to use them

Hey guys,

So I know that there are (among others) four types of distributions of data:

1. Binomial distribution
2. Poisson distribution
3. Geometric distribution
4. Exponential distribution

The exercises that I am doing for homework are repeatedly asking me to state and justify my choice of distribution, which makes it seem like there is no one correct answer. I guess that begs the question, though -- how do I know which one to choose and how do I justify my choice?

I know, for example, that the random binomial variable measures the # of successes in a fixed number of trials, geometric measures the amount of time until first success, etc. But that kinda makes it seem like my choice of distribution will always be obvious from the problem setup, i.e. there is nothing to "choose". You just know by virtue of definition.

What am I missing here? Could someone maybe give me an example where it's not immediately clear which distribution one ought to use?

Sometimes the distribution is not given to you so you how to figure it out given other information is the question.

First thing to ask, is the variable in your problem discrete or continuous? This should begin to help you narrow down the above list.

Do you know with ones are discrete/continuous?

Then ask are the trials independent? maybe time dependant?

Do you know what further impact this will have on your list?

That makes sense. Here is an example that I found from the book. It's just an exercise, and is not on my homework problem set.

Suppose that the operating lifetime of a certain type of electronic device is an exponential random variable with mean of two years. Find the probability that at least one out of 5 such devices will last over 4 years. Make sure to state and justify which distribution you use.

The prompt clearly says that the operating lifetime variable is an exponential random variable, so can the distribution actually be anything else than an exponential distribution?