if i use GEV to fit to a dataset then can i separately apply weibull distribution to the same dataset? when shape parameter is <0 in GEV,then it indicates weibull distribution

when i fit weibull distribution to a dataset using distfit it has 2 parameters. but while using gevfit it computes 3 parameters. when shape parameter is less than zero it is said it is weibull. what is the difference between the two?

Answer 1

[Debraj Maji]

Hi @Payel,

I understand that you are trying to differentiate between `gevfit` and `fitdist` and also to know whether or not it is possible to apply weibull distribution to the same dataset.

The difference betweenn 'gevfit' and 'fitdist' lies in the fundamental way the dataset is fit into the distribution which can be concisely summarised as follows:

• When fitting a Weibull distribution using `fitdist`, it estimates two parameters(shape parameter and scale parameter) to define the distribution that best fits the data.
• The Generalized Extreme Value Distribuiton estimates 3 parameters to define the distribution that best fits the data namely: the location parameter (commonly denoted as "μ"), the scale parameter (commonly denoted as "σ"), and the shape parameter (commonly denoted as "ξ").
• When the shape parameter (ξ) in the GEV distribution is less than zero, it indicates that the distribution is Weibull. Specifically, when ξ is less than zero, the GEV distribution reduces to the Weibull distribution.

The answer to your question therefore is yes, it is possible to separately use 'gevfit' and 'distfit' to the same dataset. However the best possible workflow should be according to the following steps:

1. Use 'gevfit' to fit a GEV distribution to your dataset. This will provide you with the parameters of the GEV distribution, including the shape parameter (ξ).
2. If the shape parameter (ξ) is less than zero, you can separately apply a Weibull distribution to the same dataset. You can use the estimated scale and shape parameters from the GEV fitting to initialize the parameters for the Weibull distribution, as the Weibull distribution is a special case of the GEV distribution when ξ is less than zero.
3. Fit a Weibull distribution to the dataset using the estimated parameters or by re-estimating the parameters specifically for the Weibull distribution using the 'fitdist' function. This will help you to evaluate how well the Weibull distribution describes the dataset when the shape parameter is less than zero.

For more information on the `gevfit` and `fitdist` function you cab refer to the following documentation:

• 'fitdist': https://in.mathworks.com/help/stats/fitdist.html?searchHighlight=fitdist&s_tid=srchtitle_support_results_1_fitdist
• 'gevfit': https://in.mathworks.com/help/stats/gevfit.html?s_tid=doc_ta

I hope this resolves your query.

With regards,

Debraj.

[Payel]

Thanks