#
Make Dispersion Data

When I use sample data and real data to study new method of data analysis and
simulation
, the data often comfuses me to understand the method because the data is not simple.

##
Uniform Random Value

Many programming languages have the function to make random value.

In Excel, the function

**=Rand()**

gives a value of random values from 0 to 1.

This value could be used as the value of probability.

##
Random Value of Normal Distribution

###
By Probit Transformation

By
Probit Transformation
, we can get the random value of nomal distribution.

In Excel,

**=Norminv(Rand(),0,1)**

gives us a value sampled from normal distribution (average = 0, standard deviation = 1).

For example, if we make
Histogram
by 100 values made by this method, we confirm that normal distribution is made.

###
By Logit Transformation

By
Logit Transformation
, we can get the data similar to normal distribution.

In Excel, for example,

A1 cell is "=rand()",

B1 cells is "
=LN(A1/(1-A1)))
",
we get the value.

If we make many values by this method, we can get the ditribution "average = 0, standard deviation = 1.8".

Many programming languages have functions for uniform random values and logarithm.
If the language do not have like the funcion "norminv" in Excel, logit transformaion is useful.

##
Other Values Changed From Random Value of Normal Distribution

The method to make random value of normal distribution is used to make other types.

###
Random Value of Chi-square Distribution

Square values of normal distribution is value of Chi-square distribution.

###
Data for Extreme Value Statistics

The data of
extreme value statistics
is made repeat to make normal distribution data.

###
Data of Abnormal Outlier

To study the methods for
Judge of Outlier
, abnormal outlier is useful.

For example,

=IF(**RAND()>**0.99,NORMINV(RAND(),0,1)***100**,NORMINV(RAND(),0,1))

NEXT Random Walk Model