# Common Green Belt Distributions Part 3: Poisson

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00:00

Hi, guys. Welcome back to the lean six Sigma Green belt. I'm Katherine McKeever, And today we're going to go over the last of your common, um, greenbelt distribution.

00:09

So we're gonna go over the points on distribution, which is pronounced poise Han as in French, not poison. Um, we're gonna understand it. Hopefully and we're going to recognize when we see it. So I have a confession to tell you. I hate this distribution. Hate, hate, hate. Hey, it, um

00:28

And this one actually was the distribution that almost made me reconsider my career and continuous improvement and drop out of my green belt program.

00:37

So, you know, no pressure there. Thankfully for you guys, you are learning Greenbelt much further in the future. On there are far more that analytic tools available. So you don't have to calculate this by hand, nor would I ever impose that on any of you.

00:53

All right, so the boys on distribution is still discrete data. It is account of independent events. When we talk about independent events, we talk about events that are not connected to each other in any way. So say my car accidents on the way in tow. work,

01:11

You can make an argument that are external factors

01:15

like I'm a bad driver. But whether or not I have a car accident that day seems to be left up to fate. These were going to be the ones that are in your points on distribution. They do need to be randomly occurring. So if we know that I have a car accident every Monday,

01:32

there is a pattern. Remember, we like to see patterns, so it is no longer randomly occurring.

01:37

They need to have infinite trials. So this is different than the by. No meal where we're like Oh, yeah, we do. We're gonna flip a coin 10 times. At any point in time. We needed to be able to have the opportunity

01:51

to have either on one day. I don't have this. Many cars were just making an example. One day I have one car accident or I could have 1000 and 12.

02:00

So infinite type trials. What makes this one special is it is time bound. So you will notice when I say things like one day, what we're looking for is a start in a stop. This is an equal. This is a look back

02:16

distribution. And it's really important when I show you it for you to kind of think about what does a look back distribution look like?

02:23

Well, we're starting to think about probability you can mathematically derived this when you're mean, equals your variant. So if you remember in your buying no, by no meal you're mean is larger than your variant. If you're meaning, your variant are the same here. You're probably working with the poised on, in which case,

02:43

Lord, healthier.

02:44

All right,

02:46

so here is your poison distributions. You will notice a couple of things. There are three graphs on here. This has to do with your time bound aspect. So your red line is one measure of that time period.

03:05

Your green line is four measures of a comparable time period. Either we're looking at four days

03:10

or as you will see on our next slide for years, because this really only pops up in a couple of places and then your black line is 10 something really important to know. Remember how we said that all data eventually normalizes?

03:27

This is an example. It's not super great because we know that we need a much larger sample size

03:31

the police son distribution. You will never have a giant enormous sample size. If you do, it is probably not randomly occurring, and it's not going to be a good candidate for the police on distribution.

03:46

So all of you is really exciting things in your life.

03:51

Here is where you see the poison distribution.

03:53

It is an aspect of risk mathematics or risk management. It is most commonly called the hurricane distribution, which is why we used car accidents instead of hurricane. So we didn't have our spoiler. We use this because as we continue to gather data,

04:12

the model becomes more refined.

04:15

So if you think back to our last night, we had one hurricane season, which gave us a sense of what is the probability that we're going to have a hurricane in this season? Then we looked at four. Then we looked at 10 years of data, so it became more refined as we collected more data.

04:30

The idea is as it continues to refine,

04:34

it's going to give us a sense off how many times we can expect an event in a set unit, and I say this is usually time replaced because it works both ways. You can look at a geographical slice of space, such as earthquakes along the San Andreas fault.

04:55

Or you can look at a time

04:57

such as tornadoes during tornado season along the alley. But there needs to be set parameters. And then when I say that it's time bound, you need that time aspect so you know when to restart again. So either monthly yearly,

05:15

whatever hurricane season is, I think it's four months. But you know what those time parameters are?

05:19

The longer you run this distribution, the more refined your model is. But you will notice that is still not perfect. So if you think about our major tropical storms or hurricanes, they say that we have a probability of having Teoh.

05:36

But until the season's over, we don't know if we actually had to.

05:42

That's why this is a look back distribution. We can't count it until it's happened. So it's beginning to introduce us to this idea of predictive or inferential modeling. But this one is very, very challenging to calculate because of those external factors and it being randomly occurring.

06:02

So with that, we wrapped up your common greenbelt distributions, the ones that are normal. We finished the points on distribution. You heard my SOB story that this is a very challenging distribution to use, which is why we primarily see it in risk mathematics.

06:19

And we're going to move on to our next model, which is a typical distributions. And it's really exciting for me because a typical distributions

06:28

is where we get to do a lot of our analysis work.

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