dtn.mix: Density of noncental t-normal mixture

Description

Density of noncentral t-distribution, with noncentrality parameter (NCP) being normally distributed. This is a scaled noncentral t-density.

Usage

dtn.mix(t, df, mu.ncp, sd.ncp, log = FALSE, approximation = c("int2", 
        "saddlepoint", "laplace", "none"), ...)

Arguments

A numeric vector of quantiles

A numeric vector of degrees of freedom

mu.ncp

A numeric vector of normal mean of NCP

sd.ncp

A numeric vector of normal SD of NCP

log

logical; if TRUE, log density is returned.

approximation

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 approx

...

other arguments passed to dt.int2 or dt.sad.

Value

numeric vector of densities

Details

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.

References

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 (in press).