Choosing Normalization to Create Bell Curve with Mean 1

In summary, the conversation discusses the use of a 40*40 matrix with elements close to 1 on the diagonal and small off-diagonal elements. The determinant of these randomly generated matrices is roughly the squared multiplication of the diagonal elements. When plotted on a histogram, the determinant values increase from zero to a maximum and then decrease to zero, with a mean of 1 and a peak around 0.1. The question arises about how to normalize the values to create a bell curve with a mean of 1. One suggestion is to take the logarithm of the determinant values, potentially adding a constant to achieve the desired mean. It is also mentioned that if the determinant values follow a distribution such as D~Prod(1+
  • #1
vaibhavtewari
65
0
I have a 40*40 matrix which has elements very close to 1 on diagonal and very small off-diagonal elements.
I find determinant of many of these randomly generated matrix, determinant is roughly multiplication of diagonal matrix squared. As (.95)^40 is a small number and (1.05)^40 is a bignumber, I get a histogram that increases from zero reaches a maxima and then fall to zero when I plot all these determinant values. It has a mean of 1 but peak at around .1

What kind of nomalization should I use such that when I make histogram it looks like a bell curve with a mean of 1.
 
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  • #2
Are you using the term "normalization" to refer to a change of variable meets very specific technical requirements or would you be happy with "any old change of variable"?

You could histogram the logarithms of the determinant values. That might be bell shaped. You would probably have to add some constant to the logs to get the mean to be 1.
 
  • #3
If you mean D~Prod(1+eps.Bjj) or D~Prod(1+eps.Bjj)^2 where B is a random matrix, that would be approximately lognormal (use CLT on log(D)).
 

Related to Choosing Normalization to Create Bell Curve with Mean 1

1. What is normalization and why is it important in creating a bell curve with mean 1?

Normalization is a statistical technique used to transform data into a standardized format. In creating a bell curve with mean 1, normalization is important because it ensures that the data is evenly distributed around the mean, making it easier to interpret and compare with other data sets.

2. How does normalization help in creating a bell curve with mean 1?

Normalization helps in creating a bell curve with mean 1 by adjusting the data values to fit within a specific range, typically between 0 and 1. This ensures that the data is centered around the mean and follows a normal distribution, resulting in a symmetrical bell curve.

3. What are the different normalization methods used to create a bell curve with mean 1?

There are various normalization methods that can be used to create a bell curve with mean 1, such as z-score normalization, min-max normalization, and decimal scaling. Each method has its own formula and approach, but they all aim to standardize the data and center it around the mean.

4. Can normalization be used for any type of data?

Normalization can be used for any type of data, as long as the data follows a continuous distribution. This means that it can be applied to numerical data, such as age, height, or income, but not to categorical data, such as gender or nationality.

5. Is normalization the only way to create a bell curve with mean 1?

No, normalization is not the only way to create a bell curve with mean 1. Other methods, such as standardization, can also be used to achieve a similar result. However, normalization is a commonly used technique and is often preferred due to its simplicity and ability to work with a wide range of data sets.

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