The Beta Distribution is a continuous distribution that has both upper and lower finite bounds.
Because many real situations can be bounded in this way, the Beta distribution can be used empirically to estimate the actual distribution before much data is available. Even when data is available, this distribution should fit most data in a reasonable fashion, although it may not be the best fit.
As can be seen in the examples above, This distribution can approach zero or infinity at either of its bounds, with p controlling the lower bound and q controlling the upper bound. Values of p,q<1 cause the Beta distribution to approach infinity at that bound. Values of p,q>1 cause the Beta distribution to be finite at that bound.
Beta distributions have many, many uses such as to model distributions of hydrologic variables, logarithm of aerosol sizes, activity time in PERT analysis, isolation data in photovoltaic system analysis, porosity / void ratio of soil, phase derivatives in communication theory, size of progeny in Escherichia Coli, dissipation rate in breakage models, proportions in gas mixtures, steady-state reflectivity, clutter and power of radar signals, construction duration, particle size, tool wear, and others. Many of these uses occur because of the doubly bounded nature of the Beta distribution.