  The double Pareto distribution is a heavy-tailed distribution with a
power-law tail, that is generated via geometric Brownian motion with an
exponentially distributed observation time. In this study, we examine a
modified model wherein the exponential distribution of the observation time is
replaced with a continuous uniform distribution. The probability density,
complementary cumulative distribution, and moments of this model are exactly
calculated. Furthermore, the validity of the analytical calculations is
discussed in comparison with numerical simulations of stochastic processes.
