# Find the parameter estimates for a Weibull Distribution

I am a new member of this community and I try to learn Mathematica Software.

At moment I try to find the parameter of a Weibull distribution, but I cannot solve the problem.

This is the code and the data:

data = {2, 4, 3, 1, 2, 0, 3, 3, 0, 2, 0, 4, 2, 1, 1, 1, 2, 0, 5, 2, 3,
0, 2, 2, 1, 0, 1, 3, 2, 0, 3, 3, 3, 1, 1, 2, 2, 0, 1, 2, 0, 2, 2,
0, 0, 4, 0, 4, 2, 2, 0, 0, 1, 1, 2, 1, 3, 2, 1, 0, 0, 1, 0, 2, 0, 4,
2, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 0, 4, 2,
3, 3, 1, 1, 2, 4, 4, 2, 0, 1, 1, 0, 2, 3, 2, 0, 2, 1, 1, 2, 2, 1, 5,
1, 1, 1, 3, 1, 0, 3, 0, 1, 3, 1, 2, 3, 0, 0, 3, 2, 3, 1, 2, 0, 2,
1, 3, 0, 3, 4, 1, 3, 3, 2, 0, 2, 1, 2, 3, 0, 1, 2, 1, 1, 0, 0, 2, 0,
1, 2, 1, 1, 2, 1, 0, 2, 3, 3, 5, 0, 0, 2, 2, 3, 4, 3, 1, 3, 0, 1,
1, 2, 1, 0, 3, 1, 1, 0, 1, 0, 3, 4, 2, 2, 3, 0, 4, 0, 2, 0, 1, 1, 2,
1, 2, 2, 0, 1, 1, 3, 0, 1, 4, 3, 1, 3, 0, 1, 2, 1, 1, 2, 0, 1, 0,
1, 0, 1, 2, 4, 0, 0, 2, 3, 0, 0, 2, 1, 3, 1, 5, 1, 4, 1, 1, 0, 1, 2,
5, 4, 1, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 2, 3, 1, 3, 0, 0, 1, 0, 0,
3, 1, 2, 0, 4, 1, 7, 3, 0, 1, 0, 3, 1, 2, 3, 4, 0, 0, 2, 3, 0, 4, 2,
1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 2, 2, 0, 4, 2, 3, 4, 1, 2,
2, 3, 0, 0, 1, 2, 1, 3, 5, 1, 4, 6, 1, 1, 2, 2, 1, 2, 1, 4, 1, 1, 1,
1, 0, 2, 1, 1, 3, 1, 3, 1, 7, 1, 0, 2, 1}
Histogram[data, {-0.5, 10.5, 1}]
FindDistributionParameters[data, WeibullDistribution[a, b]]


You can see from the Histogram that the distribution is a Weibull, but when I run an error occurs:

FindDistributionParameters::ntsprt: "One or more data points are not in support of the distribution WeibullDistribution[a,b]."

How can I solve it?

• With all integer values you can't possibly have a Weibull distribution. Maybe a Poisson distribution? (As the mean and variance of the sample data are nearly equal and you have all integer values.) – JimB May 13 '17 at 5:19

You must have meant "Poisson" rather than "Weibull" as all of your data consists of small non-negative integers. (If you've rounded all of the data to integers, then you should make that explicit.)

To fit a Poisson distribution try

FindDistributionParameters[data, PoissonDistribution[λ]]
(* {λ -> 1.6085714285714285} *)


You could also estimate λ with

Mean[data]
(* 1.6085714285714285 *)


To perform a test to see if there is any evidence against the data being from a Poisson try

PearsonChiSquareTest[data, PoissonDistribution[λ]]
(* 0.6877269523538061 *)


The PearsonChiSquareTest` gives a P-value much larger than 0.05. The appropriate interpretation is that there is no evidence that the data is not distributed as a Poisson (as opposed to saying that the data comes from a Poisson distribution).

• Thank you very much for your answer, I solved the problem! – D. Ercole Jun 7 '17 at 20:45