KDnuggets : News : 2008 : n06 : item12  PREVIOUS  NEXT 
FeaturesFrom: Bruce RatnerDate: 12 Mar 2008 Subject: Karl Pearson: beyond his correlation coefficient Karl Pearson: Everybody Knows His Correlation Coefficient, but Not How "Close" the Binomial Distribution is to a Normal Distribution
Everybody knows that the binomial distribution is "like" a normal distribution if the number of independent trials (n) is large and the probability of success (p) on a single trial is not too near 0 or 1. Everybody knows this because Abraham De Moivre proved it to be true in 1733. Because we are always reminded that this is an approximation, there is a nagging doubt as to how close the binomial and normal distributions really are. Pearson discovered something quite remarkable: There is a case where the agreement is much, much closer than anyone would have expected. In fact, if one particular definition of "agreement" is adopted, and if p = 1/2, the "agreement" is actually exact for all n (even for n =1), providing one minor fudge factor is allowed ... Read more.

KDnuggets : News : 2008 : n06 : item12  PREVIOUS  NEXT 
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