# Correct measure of central tendency for Skewed distribution

#### Namba

##### New Member
Dear Talk Stats users,

I am trying to solve following problem. I've got a data, which has a skewed distriubution (see attachment View attachment 4876 )

Now I can not find, how to interprate correctly the central tendency of this kind of data, because, probably this type of distribution is specific or I can't find the name of distribution. Offcourse I have no Idea which meassure of variance should I use.

Please, does anybody know how to correctly descript this data?

Regards

N.

#### Miner

##### TS Contributor
Several questions: 1) Is there a physical limit at zero below which no measures are possible?; 2) Is there a detection threshold below which all readings are zero?

#### Namba

##### New Member
Dear Miner,

Q1)
Is there a physical limit at zero below which no measures are possible?

1nswer:
Yes, there is. You can not obtain values less then zero.

Q2)
Is there a detection threshold below which all readings are zero?

No, there is not. The distribution could contains data from interval <0; N> . The values of N are limited and depends on a system, which I study, but the values have to be Integers For this example it is N=2000.

To describe my problem, I study a system of particles (for example in some tube), and I study particular sphere and the number of particle in this sphere in certain time.

So the data looks like:

t/s N
1 0
2 0
3 1
4 10
5 0
. .
. .
. .

t/s-time
N-number of particles
Maybe now you can imagine what I trying to study and describe.

Again, really thanks for your consideration.

N.

Last edited:

#### GretaGarbo

##### Human
The most usual measure of centrality or location parameter is the mean, and then the median. Both are "correct" even if the distribution is skewed. The most common variance is the one where there is something divided by "n-1".

From the data and the description one can imagine that it is Poisson distributed. The maximum likelihood estimate of that parameter would be the simple mean.

(An other usual candidate is the negative binomial distribution. That gives a somewhat larger variance.)

It could also, by looking at the histogram, be a "zero-inflated Poisson distribution". That would mean that there is a mixture of two distributions; one that is Poisson distributed with a proportion of zeros (P(X=0)) that is given by the usual Poisson model, and one that is the other proportion of "the-extra-number-of-zeros". (A Bernoulli event of either; an extra zero or a usual Poisson variable.)

If that sounds to complicated just take the mean and insert that in the Poisson distribution and compute the probability of 0, the probability of 1, the probability of 2, etc.

#### Miner

##### TS Contributor
I agree with GG. You are definitely dealing with a Poisson process when you have actual counts AND you have many more zero counts than would be expected from a Poisson distribution alone. This does appear to be a Zero Inflated Model.

You would have to have one component for which it is possible to have any count, including zero, and a second process where only zero is possible. For example, in a given population of people, you could have one group that drinks alcohol and you record the number of drinks consumed per day. On any given day, they may consume zero drinks or any number of drinks. A second group never consumes alcohol, so no count other than zero is possible. Mixing these groups would yield a zero inflated Poisson model.

Since it is a mixture, your standard measures of central tendency and spread may only represent a point in time since the ratio of the two process components may vary with time.

#### hlsmith

##### Omega Contributor
Yes, GG has given you great feedback. I will point out what I don't think has bee explicitly stated, you seem to have count data. So examining distributions related to count data would be very beneficial.

#### Namba

##### New Member
Thank you for all your answers, It really helps me a lot!