# 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 