102
Statistical Methods for Estimating Petroleum Resources
Justifi cations for Using a Lognormal Distribution
To this point we have examined Q–Q plots from worldwide examples.
We shall now choose a specifi c distribution from a lognormal family
to represent a play or geological population and discuss the following
topics:
Evidence from the Q–Q plots
•
Approximation of a lognormal distribution to geological ran•
dom variables
Advantages of using a lognormal distribution
•
Estimation error resulting from lognormal distribution
•
approximation
Evidence from the Q–Q Plots
From the examples studied and the Q–Q plots constructed from the
output of the nonparametric estimation, we observed that the lognormal distribution was and still is a favorable choice among the distributions tested. The Weibull and gamma distributions usually displayed a
concave upward pattern in their Q–Q plots for the plays studied. This
concave upward feature implied that the right-hand tail of the gamma
and Weibull distributions (large size) was too short for the play data
sets tested. On the other hand, the truncated and shifted Pareto distributions exhibit an S-shaped pattern in their Q–Q plots. These patterns implied that the right-hand tail was too long for the play data
sets. For prediction of the largest pool size in the population, the truncated and shifted Pareto distribution would tend to yield a much larger
pool. Similar results were obtained by Houghton (1988) and Davis and
Chang (1989). If a distribution tail were too long or too short, then the
total resource of a play would be over- or underestimated respectively.
In most cases, the Q–Q plots of lognormal distributions are almost
straight lines.
Approximation of a Lognormal Distribution to Geological Random
Variables
Examples from the Western Canada Sedimentary Basin demonstrate
that a lognormal distribution is adequate for approximations of various large sample sets. Take the data sets from some mature plays in
the Western Canada Sedimentary Basin (Fig. 4.27), for instance. The
Statistical Methods for Estimating Petroleum Resources
Justifi cations for Using a Lognormal Distribution
To this point we have examined Q–Q plots from worldwide examples.
We shall now choose a specifi c distribution from a lognormal family
to represent a play or geological population and discuss the following
topics:
Evidence from the Q–Q plots
•
Approximation of a lognormal distribution to geological ran•
dom variables
Advantages of using a lognormal distribution
•
Estimation error resulting from lognormal distribution
•
approximation
Evidence from the Q–Q Plots
From the examples studied and the Q–Q plots constructed from the
output of the nonparametric estimation, we observed that the lognormal distribution was and still is a favorable choice among the distributions tested. The Weibull and gamma distributions usually displayed a
concave upward pattern in their Q–Q plots for the plays studied. This
concave upward feature implied that the right-hand tail of the gamma
and Weibull distributions (large size) was too short for the play data
sets tested. On the other hand, the truncated and shifted Pareto distributions exhibit an S-shaped pattern in their Q–Q plots. These patterns implied that the right-hand tail was too long for the play data
sets. For prediction of the largest pool size in the population, the truncated and shifted Pareto distribution would tend to yield a much larger
pool. Similar results were obtained by Houghton (1988) and Davis and
Chang (1989). If a distribution tail were too long or too short, then the
total resource of a play would be over- or underestimated respectively.
In most cases, the Q–Q plots of lognormal distributions are almost
straight lines.
Approximation of a Lognormal Distribution to Geological Random
Variables
Examples from the Western Canada Sedimentary Basin demonstrate
that a lognormal distribution is adequate for approximations of various large sample sets. Take the data sets from some mature plays in
the Western Canada Sedimentary Basin (Fig. 4.27), for instance. The