Please refer to the online appendix uploaded here (also available at https://sites.google.com/site/aatoda111/file-cabinet/dPlN_appendix.pdf) for details.
Oxford Bulletin of Economics and Statistics (2022)
Matsuoka Hideaki
By Toda Alexis Akira
Macroeconomic Dynamics (2017)
The cross-sectional distribution of consumption is commonly approximated by the lognormal distribution. This note shows that consumption is better described by the double Pareto-lognormal distribution (dPlN), which has a lognormal body with two Pareto tails and arises as the stationary distribution in recently proposed dynamic general equilibrium models. dPlN outperforms other parametric distributions and is often not rejected by goodness-of-fit tests. The analytical tractability and parsimony of dPlN may be convenient for various economic applications.
Toda A. (2017) A Note on the Size Distribution of Consumption: More Double Pareto than Lognormal. Macroeconomic Dynamics, 21, 1508-1518.