An *estimator* is a specific function of the random samples, of a random
variable, that statistically represents a true unknown mean. If x is a
random
variable with an associated distribution and an unknown mean, then
the function X(x_{1}, x_{2}, x_{3},...,x_{n}) is an estimator of the unknown
mean. The set {x_{1}, x_{2}, x_{3},...,x_{n}} consists of
n independent random samples selected from
the probability density distribution of x. A good estimator should be
unbiased, consistent, and efficient [Bow72]. An estimator is *unbiased* if its
expected value equals the true mean, , i.e.,

(17) |

**Collision Estimator**:

The collision estimate of K for an active batch is:

(18) |

i = all collisions for a particle in regions where fission is possible;

j = all source particles for a batch;

N = number of source particles for a batch; and

Then the quantity in equation (2.18) is the expected number of neutrons to be produced from a fission process in collision i. Hence K

**Absorption Estimator**:

The absorption estimator of K for an active batch:

(19) |

i = an analog capture event; and

= macroscopic absorption cross section.

**Track Length Estimator**:

The track length estimator for K is given by,

(20) |

d = track length segment;

i = all track length segments,d, for a particle; and

j = all source particles for a batch.

In criticality calculations at the end of each batch (or fission generations) an estimate of K is produced by each of these three estimators. The final K estimator of each type is the average over many batch K estimates. Recent studies [Urb95a] have suggested that a combination of the three estimators to be the best K estimate available. In our research work we have used the collision estimator for all criticality and perturbation calculations. It should be emphasized that for Monte Carlo criticality calculations, the final result is not a point estimate of K, but rather a confidence interval.