The article presents the application of the metalog family of probability distributions to predict the energy production of photovoltaic systems for the purpose of generating small amounts of green hydrogen in distributed systems. It can be used for transport purposes as well as to generate energy and heat for housing purposes. The monthly and daily amounts of energy produced by a photovoltaic system with a peak power of 6.15 kWp were analyzed using traditional statistical methods and the metalog probability distribution family. On this basis, it is possible to calculate daily and monthly amounts of hydrogen produced with accuracy from the probability distribution. Probabilistic analysis of the instantaneous power generated by the photovoltaic system was used to determine the nominal power of the hydrogen electrolyzer. In order to use all the energy produced by the photovoltaic system to produce green hydrogen, the use of a stationary energy storage device was proposed and its energy capacity was determined. The calculations contained in the article can be used to design home green hydrogen production systems and support the climate and energy transformation of small companies with a hydrogen demand of up to ¾ kg/day.