Distribution with upper and lower boundaries Is there any continuous distribution that has an upper level of 1 and a lower level of 0? The reason I am asking this is that I want to know the distribution of my data which shows the roll over ratio of customer deposit which might only be between 0 (means all the fund is withdrawn) and 1 (means all the fund is rolled over).
 A: There are an infinite number of continuous distributions on the range 0 to 1.
The most obvious of the widely used families would be the beta-family, but there are many others.
However, the chances that any of the well known ones will be the distribution you actually have is zero.
In fact, I bet you don't really have a continuous distribution at all, since there will likely be a nonzero proportion of the distribution exactly at both 0 and 1. That would imply you'd be better off considering a mixture of a Bernoulli and a continuous distribution on [0,1]. You might be able to get an adequate approximation to the nominally continuous portion via say mixtures of some standard distributions, such as a mixture of betas, yielding a simple finite mixture of discrete and continuous distributions for the whole thing. 
[If you're more lucky, a single continuous distribution of simple form might be a reasonable description of the part strictly between 0 and 1, but I wouldn't assume this will be the case.]
A: Some examples of continuous pdf's defined with domain of support on (0,1) are: 

Arc-Sine, Beta, Bradford, Hahn, Inverse Triangular, Kumaraswamy, Power Function, semi-circle up, semi-circle down, skew-V, standard two-sided Power, Topp-Leone, Trapezoidal, Triangular, U-quadratic, Uniform, V and so on.

For your application, you might also want to also look into censoring (or doubly censoring) the underlying random variable below at 0, and/or above at 1. 
