@article{Hertzler:57891,
      recid = {57891},
      author = {Hertzler, Greg},
      title = {A Stochastic Differential Equation for Modeling the  “Classical” Probability Distributions},
      address = {2003-02},
      number = {414-2016-26156},
      pages = {33},
      year = {2003},
      abstract = {Stochastic differential equations are a flexible way to  model continuous probability distributions. The
most  popular differential equations are for non-stationary  Lognormal, non-stationary Normal and
stationary  Ornstein-Uhlenbeck distributions. The probability densities  are known for these
distributions and the assumptions  behind the differential equations are well  understood.
Unfortunately, the assumptions do not fit most  situations. In economics and finance, prices and
quantities  are usually stationary and positive. The Lognormal and  Normal distributions are nonstationary
and the Normal and  Ornstein-Uhlenbeck distributions allow negative prices and  quantities.
This study derives a stochastic differential  equation that includes most of the classical  probability
distributions as special cases and greatly  expands the number distributions that can be used in  models
of stochastic dynamic systems.},
      url = {http://ageconsearch.umn.edu/record/57891},
      doi = {https://doi.org/10.22004/ag.econ.57891},
}