Density of noncentral t-distribution, with noncentrality parameter (NCP) being normally distributed. This is a scaled noncentral t-density.
dtn.mix(t, df, mu.ncp, sd.ncp, log = FALSE, approximation = c("int2",
"saddlepoint", "laplace", "none"), ...)A numeric vector of quantiles
A numeric vector of degrees of freedom
A numeric vector of normal mean of NCP
A numeric vector of normal SD of NCP
logical; if TRUE, log density is returned.
character; Method of approximation. int2 computes exact denstiy for integer df and polynomially interpolate to non-integer degrees of freedom.
saddlepoint computes the saddle point approximation of the noncentral t-density.
laplace computes the laplacian approximation of the noncentral t-density.
none uses the (sort of) true noncentral t-density dt function. However, if all degrees of freedom are integers, int2 will be used even if none is specified, both of which being exact.
numeric vector of densities
Mathematically, this is equivalent to dt(t/s, df, mu.ncp/s)/s where s=sqrt(1+sd.ncp*sd.ncp). But the various approximations are usually sufficient for large problems where speed is more important than precision.
Broda, Simon and Paolella, Marc S. (2007) Saddlepoint approximations for the doubly noncentral t distribution, Computational Statistics & Data Analysis, 51,6, 2907-2918.
Young, G.A. and Smith R.L. (2005) Essentials of statistical inference. Cambridge University Press. Cambridge, UK.
Qu L, Nettleton D, Dekkers JCM. (2012) Improved Estimation of the Noncentrality Parameter Distribution from a Large Number of $t$-statistics, with Applications to False Discovery Rate Estimation in Microarray Data Analysis. Biometrics. 68. 1178-1187.