We define the Pareto distribution. We find the mean and mode of the Pareto distribution for a certain range of the parameters. #mikedabkowski, #mikethemathematician, #profdabkowski, #probability
i did not understand a single word of that lmao. i was trying to find an example of the pareto distribution. for example: if 1000 scientists write 50 journal articles then how many journal articles were written by the most productive 10% of scientists. the basic algebra in this video seemed to make sense, but mostly just made me feel poorly educated haha
If we use the Pareto Principle, 80% of the results are explained by 20% of the cause, we can use these values to obtain the alpha value of 1.16096. This alpha can be used to interpolate what percent of journal articles were produced by the most productive 10% of scientists. Given that alpha is equal to ln(n)/[ln(n)-ln(s)], n is the proportion of the population that is explained by the proportion s of the population, we can do some basic algebra to find that 72.67% of the results are explained by 10% of the population under the same assumptions. We can now say that under the assumptions of the Pareto Principle, the most productive 10% of the scientists produced about 36 of the 50 journals.