Random generation for the K distribution on
df degrees of freedom having non-centrality parameter
A K distribution is the square root of a chi-square divided by its degrees of freedom. That is, if x is chi-squared on m degrees of freedom, then y = sqrt(x/m) is K on m degrees of freedom. Under standard normal theory, K is the distribution of the pivotal quantity s/sigma where s is the sample standard deviation and sigma is the standard deviation parameter of the normal density. K is the natural distribution for tests and confidence intervals about sigma. K densities are more nearly symmetric than are chi-squared and concentrate near 1. As the degrees of freedom increase, they become more symmetric, more concentrated, and more nearly normally distributed.
Number of observations. If
Degrees of freedom (non-negative, but can be non-integer).
Non-centrality parameter (non-negative).
rkay returns pseudo-randomly generated values.
Invalid arguments will result in return value NaN, with a warning.
Depends on call to analogous chi-squared functions. See
rchisq for details on non-centrality parameter calculations.
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x <- rkay(100, 20) hist(x, main="100 observations from a K(20)") # Certainly looks like it comes from a K on 20 qqtest(x, dist="kay",df=20) # for this many degrees of freedom it looks # a lot like a gaussian (normal) distribution qqtest(x, dist="gau",df=1) # But not like it came from a K on 1 degree of freedom qqtest(x, dist="kay",df=1) # # See the vignette for more on the "K-distribution" #
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