For the current pandemic, an important open problem is immunity: do people who had this disease become immune against further infections? In the immunity study, it is important to know how frequent are different levels of immunity, i.e., what is the probability distribution of the immunity levels. Different people have different rates of immunity dynamics: for some, immunity gets to the level faster, for others the immunity effect is slower. Similarly, in some patients, immunity stays longer, it others, it decreases faster. In view of this, an important characteristic is peak immunity. A recent study provides some statistics on the peak immunity. There is not enough data to provide a statistically guaranteed selection of a probability distribution, but we can already make some preliminary conclusions. Specifically, based on the available data, we argue that the COVID-19 peak immunity values follow lognormal distribution.