Are there statistics for the share of work which is put into planning, performing, analyzing and documenting of an experiment?
There is no widely applicable rule of thumb on how to allocate resources across sub-fields and individual researchers/labs, and often the percentage break-down will even vary by project. Its something you can note retrospectively, but the variance is so high as not really to be usefully communicable; if a rule of thumb existed, you should probably ignore it.

In practice, projects differ both due to the preferences, skills, and working styles of the individuals involved, and external factors of publication culture, funding, method used, and the problem itself.

As a simple example, some projects just need a lot of careful planning to make sure they come together. This is especially true when the subject of the study is difficult or otherwise expensive to work with such as expensive/rare equipment, costly chemicals, long-running computer calculations, and human beings (especially when they are from a "vulnerable population" or some risk is involved). On the other hand, sometimes planning just takes longer because the idea needs a lot of work - while on some projects it can feel like the idea is nearly fully formed from inception and things just proceed rather obviously from first principles. 

Similarly, analysis sometimes can be wrapped up in a few days - in part because of how the project was planned, and in part by the method used. In an experiment using null hypothesis testing using p-values and decision rules, if you are doing things right your analysis should be incredibly straight-forward to run because you had better have decided long in advance of getting the data what you were going to be doing, because otherwise you are doing it all wrong. But if you are doing exploratory data analysis or using various flexible modelling methodologies, analysis could go on for quite a while ("what if you included X in your analysis? what about Y? What about an interaction between X and Y?").

Similarly, writing everything up into a publication could take a few days to a few weeks for some projects/venues - or could drag on for months and years (especially true in areas like Economics, and even more true when the authors target top journals). This also varies widely depending on the project (some are just easier to describe) and the methodology (the more complex and less familiar the methods, the more work may need to go in describing it and figuring how one even should describe it). In some paradigms the analysis stage is the writing stage, while in others the papers are more formulaic with established guidelines that feel more like filling out a template. 

To restate the initial conclusion: no, there is no rule of thumb, and if there were you should ignore it. There is no Right and Proper Division of Research Labor. Instead, learn the factors of how the stages work together, what seems to work well and what doesn't, and adjust per-project, per-collaborator, and as you develop your style and skills. Importantly, learn the expectations of your mentors and collaborators on timeline and specific plans, specific to the exact project you have in mind. Often it is only when all the details are laid out clearly for someone else that you can discover that, oh my, there is no way that a certain task is going to be as fast or slow as you thought. This way you'll develop more "known knowns" and "known unknowns", and develop ways to account for them - and end up being shocked by the countless "unknown unknowns" that appear with every new experience no matter how expert you become.