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Bell curve squeed12/14/2023 Keep in mind the annual percentage increase itself is assumed to follow the normal distribution. The plotted salary histogram is available at this link:Ĭlearly, the curve is skewed towards high salary. The Python 3 program is available at this link: Then, we can plot out all the final salary and see what the distribution looks like. We will generate random numbers for p(k), calculate salary S(k), and run it numerous times. Now we could write a computer program to run an experiment. Then S(K) = S(0)p(1)p(2).p(k).Ĭlearly, the salary is the multiplication product of initial salary and all previous years’ percentage change. Let p(k) represent the percentage of salary S(k) compared with previous year’s salary S(k-1). The accumulated effect of the percentage adjustment leads to a wide gap on salary distribution. Moreover, the new salary becomes the basis for next year’s salary adjustment. Apparently, for the same percentage increase, higher previous salary leads to higher absolute increase. For example, the top performer gets 15% increase and the low performer gets 2% increase, etc. In practice, the salary is often adjusted and viewed as the percentage of change of previous salary. The performance difference is due to numerous random factors added up and follows normal distribution. Here we assume the skill and capability of all people are similar. 20, we can compare how the salary S(20) differs from each other. Suppose people have the same salary S(0) when they start working every year, work performance is reviewed and salary is adjusted after a number of years, e.g. Here, we could use a simple probability model to provide a hint what could have caused it. There are many social and economical explanations and discussions on income inequality. The inequality is astonishing when comparing the wealth of the richest people or corporate executives with the wealth of the vast majority of the rest. It is apparent that the income distribution does not follow normal distribution. Following sections discuss two examples on income and project cost distributions. It is important to understand the difference between the two types of distributions and the conditions that can lead to skewed distributions. Skewed distributions describe phenomena with uneven and unpredictable outcomes. For example, the six-sigma method in quality management. The normal distribution describes phenomena with predictable outcomes that surround the mean value. Then the resulting distribution will often become skewed. When the conditions of the central limit theorem become invalid, i.e., when the factors are When there are a number of small factors or random events affecting a phenomenon, the sum of total effect often leads to the normal distribution, such as people’s height, weight, IQ, etc. Each individual random variable, however, can follow any distribution. Its popularity is confirmed by the central limit theorem, which shows that the sum of a sequence of independent random variables follows the normal distribution. From its name “normal”, we can guess it is deemed as the most common and well-studied form of distribution. The normal distribution has a symmetric bell-shaped probability density function.
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