Fitting bimodal wind data using Weibull mixture in matlab

2022 7 29
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Hi, I have wind data that am analyzing and I intially chose Weibull distribution to fit the data. However, from the results, the wind data displays bimodal behaviour hence unimodal weibull distribution is not fitting it well. I intend to use Weibull mixture to get more accurate resukts. How can I constract Weibull mixture in matlab? Down here is a sample of what i get with unimodal weibull distribution. Kindly help anyone who can. I will really appreciate.

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KSSV
KSSV 2022-7-29

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REad about fitdist

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okoth ochola
okoth ochola 2022-7-31
Thanks KSSV, at least I have some clue, however not obvious. Do you have any other possible suggestions you share kindly

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Jeff Miller
Jeff Miller 2022-7-30

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Your sample graph is not a probability distribution, Weibull or otherwise. For a probability distribution, the vertical axis always shows some measure of probability or relative frequency--wind speed is not such a measure. Also, for a probability distribution the possible values of the variable are on the horizontal axis (I guess these values would be the possible wind speeds in your case).
Your graph seems to be a plot of average wind speed versus month, but this is not normally called a probability distribution and it isn't obvious why one might try to fit it with a Weibull distribution.
If you want to describe how wind speed varies across months, thinking of the data as a probability distribution is probably not the right way to go.

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okoth ochola
okoth ochola 2022-7-31
Hello Jeff, you are right in everything you have said, My intention of sharing was to demosntrate how the average wind speeds over the year are distributed may that garph was misleading. Am sharing another sample which has both the histogram and the fitt, you will see that the the pdf badly fitt the data
Jeff Miller
Jeff Miller 2022-8-1
Is this the histogram including scores from all 12 months? And do you think it should be fit by a mixture because the months appear different in your earlier graph?
If so, then maybe you should start by fitting 2 separate Weibulls--one Weibull for months 2 & 7-11 with the larger wind speeds and a second Weibull for the other months. Mixtures are generally used when there is no way to identify which scores come from which component of the mixture distribution. That isn't the case here, because you know (I assume) which month each score comes from.
FWIW, I don't think that this histogram will be fit well by a mixture of 2 Weibulls either. It is too flat across bins 3-7.
okoth ochola
okoth ochola 2022-8-2
Thank you Jeff, for the usefull insights. It seems you are so conversant with wind speed fitting & wind power potential estimation and your advices might really assist me in understanding my work much better. In your opinion, according to your experience, which distribution can well fitt my data. Because that is just samples of one site, the other sites I have display bimodal behaviour (that is, thay have two peaks) from preliminary results am getting. Kindly help me out. I would like to produce a quality work that I understand properly and can explain to seven year old. IThanks
Jeff Miller
Jeff Miller 2022-8-3
@okoth ochola Sorry if I gave you the wrong impression--I know a lot about probability distributions but nothing about wind measurement. The histogram you posted has an unusual shape (or at least one I do not recognize) so I am not sure how to advise you. Perhaps you can learn a lot from your data even if they do not follow one of the traditional distribution shapes (as is often the case)?
okoth ochola
okoth ochola 2022-8-4
Jeff, I understand. I hope you've not gotten me from a different perspective. Sincerely from my heart I meant well and I was impressed the way you articulated your answers. I really valued your input and I still do. You see am training to be a physicist especially in renewable energy field and so some of the tools (mathematical, statistical and softwares) I use am meeting them for the first time. So I have to learn and understand them as fast as possible before I can use them. That is why I was ready and open for any input from someone who is conversant with the tools. I have no problem in interpretation of my results. Indeed, the sample I gave had a weired behaviour that have never seen, so the most logical conclusion was perhaps the wind speed distribution follows that of mixture distribution models. With all humility, I tend to believe this contextualizes my reaction. Kindly if you have ideas that can save me out in this situation I will highly appreciate. My advisors have insisted I find a suitable model for that site and time is a constarin.

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