In a region, we have a 50 years database of flood events. Once divided by its season of occurrence, almost 70% of the events take place in autumn. The question is if we can say that such distribution is unimodal?
When locating spatially the floods, in one of the basins, the seasonal distribution is 40% one season, 30% another, and the other two seasons have a percentage of 18% and 12%. It is a bimodal occurrence or distribution?
Do we need to apply more robust statistics to speak about unimodal or bimodal distributions? If the answer is yes, can you provide some examples?
Thanks for your help!
I do not understand why you want to simplify your data in such a way?
When you distribute your events into 4 subsets (seasons), what unimodal (or) bimodal means for you?
Please specify this.
Probably, what you want to ask is whether the data should be divided into different clusters. That has a different meaning than the question about modes (which are primarily descriptive). Your context (floods) may suggest there will be other variables available, such as climate variables. These could be exploited to improve the clustering.
I would not define the data this way. But to check, you could plot all 50 years, counting how many floods on each date. Unimodal is one defined peak, not one defined season. Bimodal is two defined peaks. Polymodal has several defined peaks. One could use the annual series to plot, partial duration series such as all floods over a certain magnitude, so there could be more than one flood in some years. As suggested by Dr. Casper, describing as tendency for seasonal flooding or modality might be better if the modal term is desired. Other variables might include physiographic area, land use changes or stream type and flooding shifts due to sediment over the 50 years. It also appears within the region, there is some variance in flooding frequency by season, so that would likely dissuade from using a unimodal term.
Since 70% of the data occur in autumn, yes we can say it is unimodal based on the seasons. But within seasons we have different observed values which have 85% chance of occurring and others have 25% of occurrence. These are the values that would be meaningful when designing any flood control structure.
Thanks Kiprotich Kiptum
Thanks William F. Hansen , if we plot all 50 years then there are several peaks. The objective is to know which season has the highest occurrence of events and if there is a decadal change during the 50 years period. Then we will add more variables, such as land use or rainfall variation as the streams are ephemeral and all flooding is generated by rainfall, following suggestion by Markus C. Casper
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