Abstract
The BetaBoop(p, q, P, Q), p, q, P, Q > 0, family of random variables includes as special cases Beta(p, q) random variables, which are known to be quite versatile in modeling different randomness patterns. Some results of the multiplicative algebra of BetaBoop random variables are commented in the light of uniform order statistics. Products and products of powers and of random powers of independent standard uniforms are also investigated, namely when the exponent is either uniform or the maximum of an uniform random sample, or its probability density function is a mixture of the uniform density and the density of an extreme of two independent uniform random variables.
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