In reply to Rick Wicklin.

Thank you for your suggestion. I followed your suggestion and received a very interesting answer involving so called Tweedy distribution which is quite unique as it is a ‘distribution that supports a positive continuous response and allows for a point mass of observed zeros’, here more about it in context of GLM:
https://communities.sas.com/t5/Statistical-Procedures/What-is-the-statistical-test-to-compare-waterfall-plots-as-used/m-p/873383/emcs_t/S2h8ZW1haWx8dG9waWNfc3Vic2NyaXB0aW9ufExINkRYS0JaNkYzTDZXfDg3MzM4M3xTVUJTQ1JJUFRJT05TfGhL