creating diversity and segregation index

[Ajay Saharan]

I am using village-level data, and I have three types of social groups in the villages. I want to create two indices using them. The first one is called the social diversity (fractionalization) index.

Equation 1 gives the standard way followed in the literature for calculating it. Can someone help me in writing a code for calculating it.

Then, I want to use it in creating another index, called segregation index. This is given in the picture below

Here, 'i' is for village only, which lies in sub-district 'j'. How to code this index?

After creating these indices. I need to rescale them on a scale of 1 to 10. How to do that?

Thanks in advance

[Nick Cox]

Many commands have been written for such measures. FRA is the complement of a measure calculated by e.g. entropyetc from SSC. SEG is not familiar to me but

search diversity

leads to

https://journals.sagepub.com/doi/10....6867X221124471

which is about one versatile command -- and in turn gives many Stata-based references.

Rescaling such measures would surely muddy their interpretation as probabilities.

[Ajay Saharan]

Thanks Nick Cox