I think this is what you want:
myroot <- function(t, nu, exi, alpha){
fun <- function(t, exi, nu)
(nu+t^2)^(-(nu+1)/2)*exp(((nu+1)*exi*t)/((nu+t^2)^0.5))
res <- alpha - integrate(fun, -Inf, t, nu=2, exi=0.5)$value
return(res)
}
uniroot(myroot, c(-2, 2), nu=2, exi=0.5, alpha=.05)
Hope this is helpful,
Ravi
Ravi Varadhan, Ph.D. (Biostatistics), Ph.D. (Environmental Engg)
Associate Professor, Department of Oncology
Division of Biostatistics & Bionformatics
Sidney Kimmel Comprehensive Cancer Center
Johns Hopkins University
550 N. Broadway, Suite 1111-E
Baltimore, MD 21205
410-502-2619
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