RMI Nuclear Justice Documents

Parameters were calculated from EX and c for the gamma distribution as:
a = L/c?

B = EX of

In simulations where EX was selected from a uniform distribution, a and
b are defined to be +50% of the desired expected value of the distribution.
For example, suppose EX is to be 10.0.
Then a = (1-0.5)10 and
b = (1+0.5)10, or EX is selected from the interval (5, 15).
The parameter
values for a, 8, uy, and o* were then calculated with the formulas given
above to generate bne realization of x.

The infinite series,

(t), necessary to calculate E(x) assuming lognor-

mality was evaluated to a point where the ratio of an additional term to
the summation was less than 1E-7.
Values of the t-statistic were obtained
from tabled values.

RESULTS AND DISCUSSION

In general, the expected value of the distributions had no effect on the
results. Rather, the coefficient of variation tended to explain the

observed phenomena.
Hence in the following sections, the statements
made will apply to the range of expected values simulated.
A complete
listing of the simulation results is given in White (in preparation).
Gamma Estimator With Gamma Distributed Data

The arithmetic mean is an unbiased estimator for EX, and so the simulations showed.
Of course, individual point estimates may vary widely.
Hence, the main purpose of simulating this estimator was to check the
achieved coverage against the predicted value.
A gradual decline in
achieved coverage was noted with an increase in the coefficient of
variation (Fig.

4).

However,

coverage is greater than 70%.

for all cases simulated,

the achieved

A slight decline in achieved coverage is

noted also for decreasing sample sizes.
c = 2 than any other case.

This trend is more apparent for

Lognormal Estimator for LognormallyDistributed Data
Because this estimator is MVUE for lognormally distributed data, the
chief purpose for the simulation was to check the coverage of the confi~
dence interval.
The achieved coverage is always close to the predicted
954 for n = 100.
However, the achieved coverage declines with decreasing

618