dDtrend | R Documentation |
This function computes \Pr(D = k), i.e. the probability mass function for D=∑_{i=1}^{n} (R_i - i)^2, the nonparametric trend statistic proposed by \insertCiteLehmann75;textualskedastic, under the assumption that the ranks R_i are computed on a series of n independent and identically distributed random variables with no ties.
dDtrend(k = "all", n, override = FALSE)
k |
An integer of |
n |
A positive integer representing the number of observations in the series. Note that computation time increases rapidly with n and is infeasible for n>11. |
override |
A logical. By default, the function aborts if n > 11
due to the prohibitively slow computation (which may cause some systems
to crash). Setting this argument to |
The function is used within horn
in computing
p-values for Horn's nonparametric test for heteroskedasticity in a
linear regression model \insertCiteHorn81skedastic. The support of
D consists of consecutive even numbers from 0 to
\frac{n(n-1)(n+1)}{3}, with the exception of the case n=3,
when the value 4 is excluded from the support. Note that computation speed
for k = "all"
is about the same as when k
is set to an
individual integer value, because the entire distribution is still
computed in the latter case.
A double vector containing the probabilities corresponding to the
integers in its names
attribute.
horn
prob <- dDtrend(k = "all", n = 6) values <- as.integer(names(prob)) plot(c(values[1], values[1]), c(0, prob[1]), type = "l", axes = FALSE, xlab = expression(k), ylab = expression(Pr(D == k)), xlim = c(0, 70), yaxs = "i", ylim = c(0, 1.05 * max(prob))) axis(side = 1, at = seq(0, 70, 10), las = 2) for (i in seq_along(values)) { lines(c(values[i], values[i]), c(0, prob[i])) }
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