
Consider the product
pprodn2(x, rho)
pprodt2(x, rho, nu)
qprodt2(p, rho, nu, tol=1e-5, trace=0)
a numeric vector
a numeric vector
a numeric vector of probabilities
a scalar value representing the correlation (or the matching term in the t case when correlation does not exists)
a positive scalar representing the degrees of freedom
the desired accuracy (convergence tolerance),
passed to function uniroot
integer number for controlling tracing information,
passed on to uniroot
Adelchi Azzalini
Function pprodt2
implements formulae in Theorem 1 of Wallgren (1980).
Corresponding quantiles are obtained by qprodt2
by solving the
pertaining non-linear equations with the aid of uniroot
,
one such equation for each element of p
.
Function pprodn2
implements results for the central case in
Theorem 1 of Aroian et al. (1978).
Aroian, L.A., Taneja, V.S, & Cornwell, L.W. (1978). Mathematical forms of the distribution of the product of two normal variables. Communications in statistics. Theory and methods, 7, 165-172
Wallgren, C. M. (1980). The distribution of the product of two correlated t variates. Journal of the American Statistical Association, 75, 996-1000
p <- pprodt2(-3:3, 0.5, 8)
qprodt2(p, 0.5, 8)
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