The Doubly-Pareto Uniform Distribution with Applications in Uncertainty Analysis and Econometrics

In this paper we propose a novel four parameter continuous univariate distribution that can be motivated from at least two approached. The first one views the distribution as a generalization of the uniform one that allows for uncertainty specification at the vicinity of its bounds (gradually) represented via two Pareto tails. The second one is that of an asymmetric heavy-tailed, peaked distribution with an unbounded domain with the property that the location of the mode is not uniquely determined but rather is described by an uniform range. Properties of the distribution are described and a maximum likelihood estimation (MLE) procedure for the mode location and the Pareto tails parameters is presented. The procedure is illustrated by means of an i.i.d. sample of standardized log-differences of bi-monthly 30-year US certificate deposit interest rates for the period from 1964-2004. The sample is constructed utilizing the Auto-Regressive Conditional Heteroscedastic (ARCH) time series model devised by the Nobel Laureate R.F. Engle (1982). Mathematics Subject Classification (2000). Primary 99Z99; Secondary 00A00.