3. EXAMPLES OF MLE | KOLMOGOROV’S
LAW OF FRAGMENTATION
Kolmogorov’s law of fragmentation states that the size of an
individual particle in a large collection of particles resulting from
the fragmentation of a mineral compound will have an
approximate lognormal distribution.
A random variable X is said to have a lognormal distribution if
log(X) has a normal distribution.
The law was first noted empirically and then later given a
theoretical basis by Kolmogorov and has been applied to a variety
of engineering studies.
For instance, it has been used in the analysis of the size of
randomly chosen gold particles from a collection of gold sand.
Another application of the law has been to a study of the stress
release in earthquake fault zones
6. CONFIDENCE INTERVALS
The point estimates say nothing about how close our estimated parameter are to the
actual value of the parameter.
Even when we can calculate the variance of the estimator, if we don’t know how its
distributed its generally impossible to say with confidence that we are close to the
actual value of the parameter.
So, it maybe more useful to give an interval where we can say with certain
confidence that the value of the unknown parameter lies.
Such an interval is called a confidence interval.
The length of the interval conveys the precision of estimation.
A short interval implies precise information.
12. CONFIDENCE INTERVAL ON THE
MEAN OF NORMAL, VARIANCE
UNKNOWN |EXAMPLE
An article in the journal Materials
Engineering (1989, Vol. II, No. 4, pp.
275– 281) describes the results of tensile
adhesion tests on 22 U-700 alloy
specimens. The load at specimen failure
is as follows (in megapascals):
