Abstract
The motivation of this paper is to show how to use the information from given distributions and to fit distributions in order to confirm models. Our examples are especially for disciplines slightly away from mathematics. One minor result is that standard deviation and mean are at most a more or less good approximation to determine the best Gaussian fit. In our first example we scrutinize the distribution of the intelligence quotient (IQ). Because it is an almost perfect Gaussian distribution and correlated to the parents’ IQ, we conclude with mathematical arguments that IQ is inherited only which is assumed by mainstream psychologists. Our second example is income distributions. The number of rich people is much higher than any Gaussian distribution would allow. We present a new distribution consisting of a Gaussian plus a modified exponential distribution. It fits the fat tail perfectly. It is also suitable to explain the old problem of fat tails in stock returns.
Highlights
In finance, economics, and many social sciences distributions are important
In our first example we scrutinize the distribution of the intelligence quotient (IQ)
Because it is an almost perfect Gaussian distribution and correlated to the parents’ IQ, we conclude with mathematical arguments that IQ is inherited only which is assumed by mainstream psychologists
Summary
Economics, and many social sciences distributions are important. there are two closely connected puzzling items. Once having accepted this derivation as correct, observations of stock prices and the like showing a fat tail are in contradiction to a Gaussian distribution From this one has an experimental proof that some assumptions of Fama [3] must be wrong. For a brief summary of the use of distributions especially in non-mathematical sciences, the purpose of this paper is not to fix the mentioned problems especially when using a Gaussian distribution wrongly or without justification.
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