Posts

Parametric Techniques on Other Distributions- THE KOLMOGOROV-SMIRNOV (K-S) TEST

Image
Parametric Techniques on Other Distributions THE KOLMOGOROV-SMIRNOV (K-S) TEST The chi-square test is no doubt the most popular of all methods of  comparing two distributions. Since many market-oriented applications  other than the ones . However, the best test for our pur poses may well be the K-S test. This very efficient test is applicable to  unbinned distributions that are a function of a single independent vari able.  All cumulative density functions have a minimum value of 0 and a  maximum value of 1. What goes on in between differentiates them. The  K-S test measures a very simple variable, D, which is defined as the  maximum absolute value of the difference between two distributions'  cumulative density functions.  To perform the K-S test is relatively simple. N objects are standardized  and sorted in ascending order.  As we go through  these sorted and standardized trades, the cumulative probability is how ever many trades we've gone through divided b

Parametric Optimal f on the Normal Distribution- FURTHER DERIVATIVES OF THE NORMAL

Image
Parametric Optimal f on the Normal Distribution FURTHER DERIVATIVES OF THE NORMAL Sometimes you may want to know the second derivative of the N(Z)  function. Since the N(Z) function gives us the area under the curve at Z,  and the N'(Z) function gives us the height of the curve itself at Z, then  the N"(Z) function gives us the instantaneous slope of the curve at a  given Z: N"(Z) = -Z/2.506628274*EXP(-(Z^2/2) where, EXP() = The exponential function. To determine what the slope of the N'(Z) curve is at +2 standard  units: N"(Z) = -2/2.506628274*EXP(-(+2^2)/2)            = -212.506628274*EXP(-2)            = -2/2.506628274*.1353353            = -.1079968336 Therefore, we can state that the instantaneous rate of change in the  N'(Z) function when Z = +2 is -.1079968336. This represents rise/run,  so we can say that when Z = +2, the N'(Z) curve is rising -.1079968336  for ever) 1 unit run in Z.  Figure  N"(Z) g