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