# Extreme Value Statistics

For example, the data,
"Max temperture every year" and "The longest length of the parts"
are set of maximum data.

Extreme value statistics studies the data set of maximum or minimum.
It studies the boundary are between major area of the distribution and
Outlier.

It is used as the method to design the height of walls and weakness of parts.

##
Distribution of Exterme Values

For example, max data from many normal distribution of same average and standard deviation
is not the symmetry.
(see
Made by Normal Distribution But Not Normal Distribution
)

We can use this distribution as the mathematical formulaiton.
by extreme value statistics.

##
History

The weakness of the chane depends on the most weak point.
It is studied in
Reliability Engineering
.

Next, it is found that the distribution of extreme values are only three types.

Next, the three types could be written by one formulation.
It is calle GEV (generalized extreme value distribution).

Recently, not only max data but the second, the third and so on are used to estimate the ditstribution of extreme area.

NEXT Chebyshev's inequality