Dear Francisco, if you take X, Y, Z, distance and weight as single variables you can go with k-means clustering which should give you a clustered density of the data.

Fractal analysis could be an option, assuming that you are interested in a general quantification 

There really isn't enough information for us to recommend a "best" method of evaluation. I really depends on the nature of the data (point or jurisdictional), scale (smaller scale with greater distances or large scale with micro', neighborhood distances). It depends on what you want to ask the data that you have. In some cases, a series of intelocking buffers may be all you need. In others, one or another kind of cluster analysis may serve. And ... is the data raster or vector. They can be transposed but the medium will help serve to define the approach. Finally, what is it you want to ask of the data? Is it incidence and density or is it incidence and density in relation to some other factor (for example, mortality in a landscape of relative wealth or poverty). 

So the problem isn't with suggestions...there are lots. But it is about knowing (you and we) what you're looking at and the thing you're looking for.

Tom, you're absolutely right. I did not give enough detail to understand how to evaluate my dataset.

I have geo-referenced data points of each fishing haul by a fishing fleet. The weight value of each point is the catch taken.

I quickly noticed that some years fishing hauls are scattered in the area of fishing, while another year seen very concentrated. Moreover, when they are concentrated, the catch is greater.

I'm trying to find some statistical index that allows me to compare these two patterns.

You can take all the points, calculate the convex hull then divide the yearly catch weight by the area of the yearly convex hull. A more stochastic approach could be that for each year you pick randomly 3 points, then divide the total catch weight at these points by the area of the triangle they form.

Yavor, your first approach seems interesting.

Do you have any idea how to include the number of points into the equation?

You can divide the number of points by the convex hull area to get something analogous to density but if you just use the sun of the total catch weight is also similar, the bigger the number of points the bigger the sum of all catches. A problem with this approach could be that the convex hull shape is susceptible to outliers. That's why maybe you could bootstrap the points and get an average volume.

 It is attached an example of the convex hull method.

Globally, provides a good approximation of the spatial pattern of catches.

In year 1, the area of the convex hull is higher but the catch is smaller, therefore the index (I) is smaller. The opposite occurs in the year2. This allows a comparison between years.

My new question is about how to make a finer analysis of this pattern. For example in year 2, the capture was greater and occurred in a smaller area. Are there other indices that also consider the level of proximity between points? Or, is there any method to define areas of highest concentration of catch?.

You can look into alpha-shapes, these are essentially non-convex polygons with a specific radius. Another measure you can look into is the D0 dimension, you cover the region with boxes of specific size and see how the number of non-empty boxes scales with the box size. This is called the capacity dimension of a spatial point distribution.