Quantile for the Distribution of Product of Two Normal Variables
Generates quantiles for the distribution of product of two normal random variables
qprodnormal(p, mu.x, mu.y, se.x, se.y, rho=0, lower.tail=TRUE, type="dop", n.mc=1e5)
p |
probability |
mu.x |
mean of x |
mu.y |
mean of y |
se.x |
standard error (deviation) of x |
se.y |
standard error (deviation) of y |
rho |
correlation between x and y, where -1 <
|
lower.tail |
logical; if |
type |
method used to compute P[X*Y < q]. It takes on
the values |
n.mc |
when |
This function returns a quantile and the associated error (accuracy) corresponding
the requested percentile (probability) p of the
distribution of product of mediated effect (product of two normal random
variables). To
obtain a quantile using a specific method, the argument type
should be specified. The default method is type="dop", which uses the method described
by Meeker and Escobar (1994) to evaluate the CDF of the distribution
of product of two normal variables. type="MC" uses the Monte
Carlo approach (Tofighi & MacKinnon, 2011). type="all" prints
quantiles using all three options. For the method type="dop", the
error is the modulus of absolute error for the numerical
integration (for more information see Meeker and Escobar, 1994). For
type="MC", the error refers to the Monte Carlo error.
An object of the type list that contains the
following values:
q |
quantile corresponding to probability |
error |
estimate of the absolute error |
Davood Tofighi dtofighi@unm.edu and David P. MacKinnon davidpm@asu.edu
MacKinnon, D. P., Fritz, M. S., Williams, J., and Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39, 384–389.
Meeker, W. and Escobar, L. (1994). An algorithm to compute the CDF of the product of two normal random variables. Communications in Statistics: Simulation and Computation, 23, 271–280.
Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x
##lower tail qprodnormal(p=.1, mu.x=.5, mu.y=.3, se.x=1, se.y=1, rho=0, lower.tail = TRUE, type="all") ##upper tail qprodnormal(p=.1, mu.x=.5, mu.y=.3, se.x=1, se.y=1, rho=0, lower.tail = FALSE, type="all")
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