『**(Abstract)**

The U.S. Geological Survey procedure for the estimation of the
general form of the parent distribution requires that the parameters
of the log-geometric distribution be calculated and analyzed for
the sensitivity of these parameters to different conditions. In
this study, we derive the shape factor of a log-geometric distribution
from the ratio of frequencies between adjacent bins. The shape
factor has a log straight-line relationship with the ratio of
frequencies. Additionally, the calculation equations of a ratio
of the mean size to the lower size-class boundary are deduced.
For a specific log-geometric distribution, we find that the ratio
of the mean size to the lower size-class boundary is the same.
We apply our analysis to simulations based on oil and gas pool
distributions from four petroleum systems of Alberta, Canada and
four generated distributions. Each petroleum system in Alberta
has a different shape factor. Generally, the shape factors in
the four petroleum systems stabilize with the increase of discovered
pool numbers. For a log-geometric distribution, the shape factor
becomes stable when discovered pool numbers exceed 50 and the
shape factor is influenced by the exploration efficiency when
the exploration efficiency is less than 1. The simulation results
show that calculated shape factors increase with those of the
parent distributions, and undiscovered oil and gas resources estimated
through the log-geometric distribution extrapolation are smaller
than the actual values.

Key Words: Pareto; shape factor; simulation; sensitivity analyses;
resource appraisal.』

**Introduction
Parameter derivations
** The shape factor

The ratio of the mean size to the lower size-class boundary

Precision of parameters

Generated distributions

Different discovery process

Different parent distributions

Conclusions

Acknowledgments

References