coversim | R Documentation |
Creates a confidence region and determines coverage results for a corresponding point of interest.
Iterates through a user specified number of trials.
Each trial uses a random dataset with user-specified parameters (default) or a user specified dataset
matrix ('n'
samples per column, 'iter'
columns) and returns the corresponding actual coverage results.
See the CRAN website https://CRAN.R-project.org/package=conf for a link to a coversim
vignette.
coversim(alpha, distn, n = NULL, iter = NULL, dataset = NULL, point = NULL, seed = NULL, a = NULL, b = NULL, kappa = NULL, lambda = NULL, mu = NULL, s = NULL, sigma = NULL, theta = NULL, heuristic = 1, maxdeg = 5, ellipse_n = 4, pts = FALSE, mlelab = TRUE, sf = c(5, 5), mar = c(4, 4.5, 2, 1.5), xlab = "", ylab = "", main = "", xlas = 0, ylas = 0, origin = FALSE, xlim = NULL, ylim = NULL, tol = .Machine$double.eps ^ 1, info = FALSE, returnsamp = FALSE, returnquant = FALSE, repair = TRUE, exact = FALSE, showplot = FALSE, delay = 0 )
alpha |
significance level; scalar or vector; resulting plot illustrates a 100(1 - |
distn |
distribution to fit the dataset to; accepted values: |
n |
trial sample size (producing each confidence region); scalar or vector; needed if a dataset is not given. |
iter |
iterations (or replications) of individual trials per parameterization; needed if a dataset is not given. |
dataset |
a |
point |
coverage is assessed relative to this point. |
seed |
random number generator seed. |
a |
distribution parameter (when applicable). |
b |
distribution parameter (when applicable). |
kappa |
distribution parameter (when applicable). |
lambda |
distribution parameter (when applicable). |
mu |
distribution parameter (when applicable). |
s |
distribution parameter (when applicable). |
sigma |
distribution parameter (when applicable). |
theta |
distribution parameter (when applicable). |
heuristic |
numeric value selecting method for plotting: 0 for elliptic-oriented point distribution, and 1 for smoothing boundary search heuristic. |
maxdeg |
maximum angle tolerance between consecutive plot segments in degrees. |
ellipse_n |
number of roughly equidistant confidence region points to plot using the elliptic-oriented point distribution (must be a multiple of four because its algorithm exploits symmetry in the quadrants of an ellipse). |
pts |
displays confidence region boundary points if |
mlelab |
logical argument to include the maximum likelihood estimate coordinate point (default is |
sf |
significant figures in axes labels specified using sf = c(x, y), where x and y represent the optional digits argument
in the R function |
mar |
specifies margin values for |
xlab |
string specifying the horizontal axis label (applies to confidence region plots when |
ylab |
string specifying the vertical axis label (applies to confidence region plots when |
main |
string specifying the plot title (applies to confidence region plots when |
xlas |
numeric in 0, 1, 2, 3 specifying the style of axis labels (see |
ylas |
numeric in 0, 1, 2, 3 specifying the style of axis labels (see |
origin |
logical argument to include the plot origin (applies to confidence region plots when |
xlim |
two element vector containing horizontal axis minimum and maximum values (applies to confidence region plots
when |
ylim |
two element vector containing vertical axis minimum and maximum values (applies to confidence region plots
when |
tol |
the |
info |
logical argument to return coverage information in a list; includes |
returnsamp |
logical argument; if |
returnquant |
logical argument; if |
repair |
logical argument to repair regions inaccessible using a radial angle from its MLE (multiple root azimuths). |
exact |
logical argument specifying if alpha value is adjusted to compensate for negative coverage bias in order to achieve (1 - alpha) coverage probability using previously recorded Monte Carlo simulation results; available for limited values of alpha (roughly <= 0.2–0.3), n (typically n = 4, 5, ..., 50) and distributions (distn suffixes: weibull, llogis, norm). |
showplot |
logical argument specifying if each coverage trial produces a plot. |
delay |
numeric value of delay (in seconds) between trials so its plot can be seen (applies when |
Parameterizations for supported distributions are given following
the default axes convention in use by crplot
and coversim
, which are:
Horizontal | Vertical | |
Distribution | Axis | Axis |
Cauchy | a | s |
gamma | θ | κ |
inverse Gaussian | μ | λ |
log logistic | λ | κ |
log normal | μ | σ |
logistic | μ | σ |
normal | μ | σ |
uniform | a | b |
Weibull | κ | λ |
Each respective distribution is defined below.
The Cauchy distribution for the real-numbered location parameter a, scale parameter s, and x is a real number, has the probability density function
1 / (s π (1 + ((x - a) / s) ^ 2)).
The gamma distribution for shape parameter κ > 0, scale parameter θ > 0, and x > 0, has the probability density function
1 / (Gamma(κ) θ ^ κ) x ^ {(κ - 1)} exp(-x / θ).
The inverse Gaussian distribution for mean μ > 0, shape parameter λ > 0, and x > 0, has the probability density function
√ (λ / (2 π x ^ 3)) exp( - λ (x - μ) ^ 2 / (2 μ ^ 2 x)).
The log logistic distribution for scale parameter λ > 0, shape parameter κ > 0, and x ≥ 0, has a probability density function
(κ λ) (x λ) ^ {(κ - 1)} / (1 + (λ x) ^ κ) ^ 2.
The log normal distribution for the real-numbered mean μ of the logarithm, standard deviation σ > 0 of the logarithm, and x > 0, has the probability density function
1 / (x σ √(2 π)) exp(-(\log x - μ) ^ 2 / (2 σ ^ 2)).
The logistic distribution for the real-numbered location parameter μ, scale parameter σ, and x is a real number, has the probability density function
(1 / σ) exp((x - μ) / σ) (1 + exp((x - μ) / σ)) ^ {-2}
The normal distribution for the real-numbered mean μ, standard deviation σ > 0, and x is a real number, has the probability density function
1 / √ (2 π σ ^ 2) exp(-(x - μ) ^ 2 / (2 σ ^ 2)).
The uniform distribution for real-valued parameters a and b where a < b and a ≤ x ≤ b, has the probability density function
1 / (b - a).
The Weibull distribution for scale parameter λ > 0, shape parameter κ > 0, and x > 0, has the probability density function
κ (λ ^ κ) x ^ {(κ - 1)} exp(-(λ x) ^ κ).
If the optional argument info = TRUE
is included then a list of coverage results is returned. That list
includes alpha
value(s), n
value(s), coverage and error results per iteration. Additionally, returnsamp = TRUE
and/or returnquant = TRUE
will result in an n
row, iter
column maxtix of sample and/or sample cdf values.
Christopher Weld (ceweld@email.wm.edu)
Lawrence Leemis (leemis@math.wm.edu)
Weld, C., Loh, A., Leemis, L. (in press), "Plotting Likelihood-Ratio Based Confidence Regions for Two-Parameter Univariate Probability Models", The American Statistician.
crplot
, uniroot
## assess actual coverage at various alpha = {0.5, 0.1} given n = 30 samples, completing ## 10 trials per parameterization (iter) for a normal(mean = 2, sd = 3) rv coversim(alpha = c(0.5, 0.1), "norm", n = 30, iter = 10, mu = 2, sigma = 3) ## show plots for 5 iterations of 30 samples each from a Weibull(2, 3) coversim(0.5, "weibull", n = 30, iter = 5, lambda = 1.5, kappa = 0.5, showplot = TRUE, origin = TRUE)
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