We describe a set of probability distributions, dubbed compressible priors, whose independent and identically distributed (iid) realizations result in p-compressible signals. A signal x ∈ R is called p-compressible with magnitude R if its sorted coefficients exhibit a power-law decay as |x|(i) . R · i−d, where the decay rate d is equal to 1/p. p-compressible signals live close to K-sparse signa...

A new distribution called the beta-generalized Pareto is proposed. Several properties of this distribution are presented. The expressions for the mean, mean deviation, variance, and entropies are obtained. The method of maximum likelihood is proposed to estimate the parameters of the distribution. The flexibility of this distribution is illustrated in an application to a real data set.