An example of distributive justice would be a country that practices egalitarianism and mandates that all of the people living within their society should receive the same benefits and the same burdens in an equal amount. In a sense, all countries and their governments are examples of distributive justice as they must decide who is able to get specific things and how much of those things they should get.
Egalitarianism is just one form of distributive justice. Another form is socialism, which is the distribution of homes, jobs and other goods or services based on the abilities of the person and on the person's needs.
Socialism also looks to maximize the society's welfare and wants to meet all of the basic needs of the society from a biological standpoint. This differs from the egalitarianism form of distributive justice as it believes that there are ways to justify differences in the treatment of people based on their abilities and needs, while egalitarianism focuses on equal distribution for all regardless of ability or need.
Yet another form of distributive justice is known as the protestant work ethic. In this form, the distribution is given to each individual member of society based on that individual's contribution to the society through work.
There is also a libertarianism form of distributive justice that focuses on distribution from the free exchange of the people. It claims that anything that happens to the society is acceptable and just as long as it is a direct result of the free will choices that individuals have made.