dtn.mix: Density of noncental t-normal mixture

In pi0: Estimating the proportion of true null hypotheses for FDR

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

t	A numeric vector of quantiles
df	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 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.
...	other arguments passed to dt.int2 or dt.sad.

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.

Value

numeric vector of densities

Note

For normal-normal mixture, set df=Inf. When this is the case, approximation is ignored.

Author(s)

Long Qu

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. 68. 1178-1187.

See Also

dt.sad, dt.int2, dt.lap

pi0 documentation built on May 2, 2019, 4:47 p.m.