Massart Inequality for Distributions
This function implements a test of the random number generator and distribution function based on an inequality due to Massart (1990).
distIneqMassart(densFn = "norm", n = 10000, probBound = 0.001, ...)
densFn |
Character. The root name of the distribution to be tested. |
n |
Numeric. The size of the sample to be used. |
probBound |
Numeric. The value of the bound on the right hand side of the Massart inequality. See Details. |
... |
Additional arguments to allow specification of the parameters of the distribution. |
Massart (1990) gave a version of the Dvoretsky-Kiefer-Wolfowitz inequality with the best possible constant:
P(sup_x|F_n(x)-F(x)|> t) <= 2exp(-2nt^2)
where F_n is the empirical distribution function for a sample of n independent and identically distributed random variables with distribution function F. This inequality is true for all distribution functions, for all n and t.
This test is used in base R to check the standard distribution
functions. The code may be found in the file p-r-random.tests.R
in the tests directory.
sup |
Numeric. The supremum of the absolute difference between the empirical distribution and the true distribution function. |
probBound |
Numeric. The value of the bound on the right hand side of the Massart inequality. |
t |
Numeric. The lower bound which the supremum of the absolute difference between the empirical distribution and the true distribution function must exceed. |
pVal |
Numeric. The probability that the absolute difference
between the empirical distribution and the true distribution function
exceeds |
check |
Logical. Indicates whether the inequality is satisfied or not. |
David Scott d.scott@auckland.ac.nz, Christine Yang Dong c.dong@auckland.ac.nz
Massart P. (1990) The tight constant in the Dvoretsky-Kiefer-Wolfovitz inequality. Ann. Probab., 18, 1269–1283.
## Normal distribution is the default
distIneqMassart()
## Specify parameter values
distIneqMassart(mean = 1, sd = 2)
## Gamma distribution has no default value for shape
distIneqMassart("gamma", shape = 1)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.