An Interpolating Family of Size Distributions

We introduce a new five-parameter family of size distributions on the semi-finite interval $[x_0,\infty)$ with two attractive features. First, it interpolates between power laws, such as the Pareto distribution, and power laws with exponential cut-off, such as the Weibull distribution. The proposed family thus includes many well-known size distributions as special cases. Second, it has some tractability advantages over the five-parameter Generalized Beta distribution. We derive the hazard function, survival function, modes and quantiles. Moreover, we propose a random generation procedure and discuss the maximum likelihood estimation of the five parameters. Finally, we present three applications to real data from actuarial sciences, environmental sciences and survival analysis to illustrate that the interpolating family of size distributions works quite effectively.