I am looking for the (or a) suitable name of a continuous univariate distribution depending on two parameters $\alpha>0$ (shape) and $\beta >0$ (scale). The support is $(0, \,\beta)$ and the survival and density functions are $$ S_X(x) = \left[1- x/\beta\right]^\alpha \qquad f_X(x) = \frac{\alpha}{\beta}\, \left[1- x/\beta\right]^{\alpha-1} $$ This is the special case of the Generalised Pareto Distribution (GPD) with location at zero and finite upper end-point $ S_{\mathrm{GPD}}(x) = \left[1 + \xi \,x/\sigma \right]^{-1/\xi} $ with $\xi <0$, but here reparametrised through $\alpha := -1/\xi$ and $\beta:=-\sigma/\xi$. Thus the exponential distribution $\xi = 0$ is the limit $\beta \rightarrow +\infty$.
In Wikipedia's list of probability distributions, this is but a special case of Beta (rescaled) and Kumaraswamy's (rescaled).
A comparable reparametrisation for the GPD with $\xi >0$, namely $\alpha := 1/\xi$ and $\beta:=\sigma/\xi$, leads to the Lomax distribution, so a cheap pun would suggest to use ``maxlo'' distribution.
beta*rbeta(n,1,alpha)if you need to simulate it. If you need to draw inference on the parameters, you can call the function whatever you like... – Xi'an Jun 27 '12 at 18:22