A Probability Density Function: Converting Experimental Observations to PDF

[naveendeveloper]

TL;DR Summary

I am not able to understand how to convert an experiments observation of continuous random variable into probability density function

Hi All
I am currently doing Master in data science. I came across the function PDF probability density function which is used to find cumulative probability(range) of a continuous random variable.
The PDF probability density function is plotted against probability density in y-axis and Random variable in x axis.
I am not able to understand how to convert an experiments observation of continuous random variable into probability density function
Kindly help me understand with a small example
Thank you

 

[PeroK]

Do you know about the normal distribution, for example?

 

[FactChecker]

Make a histogram and divide every frequency number by the total sample size. That will approximate the PDF. The histogram cell range should be set appropriately so that there are enough samples in them so that they do not jump up and down too much and also so that there are not too few cells to approximate the continuous PDF..

 

[naveendeveloper]

Make a histogram and divide every frequency number by the total sample size. That will approximate the PDF. The histogram cell range should be set appropriately so that there are enough samples in them so that they do not jump up and down too much and also so that there are not too few cells to approximate the continuous PDF..

Hi
Thank you so much on your explanation. I have attached an excel sheet of height of 100k employees in the following link https://docs.google.com/spreadsheets/d/142Ay2BOh5rOd1weO4f7Jbe2-roYoTDRo/edit?usp=sharing&ouid=116301201506347494587&rtpof=true&sd=true
Kindly can you help me understand how to create the PDF by creating histogram and normalising its area to 1 ( just the logic to do that would be really helpful)

One other query, after creating the PDF the y-axis Probability density what does it represent

Thanks
Naveen

 

[FactChecker]

The steps would depend a lot on what statistics software package you are using. I like R, which is free, well respected, and well documented. R has a function, densityplot, that does it. I don't know what is available in EXCEL.
If you are doing it all yourself, this is a rough description of the process.
1) get the range of the height data, heightMin & heightMax.
2) divide the range evenly into some number of sub-range cells (with 1000 data points, try 20 cells as a first attempt and adjust if desired)
3) count the number of data points in each cell
4) convert the cell counts into fractions by dividing by the total number of data points (1000 in your example)
5) plot the results.

Have you had any classes in probability and statistics? The probability density function shows the fraction of results that would have certain values.