R Under development (unstable) (2024-08-16 r87026 ucrt) -- "Unsuffered Consequences"
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> library("mvtnorm")
> 
> p <- 0.8
> mean <- c(6.75044368, 0.04996326)
> sigmas <- rbind(
+   c(0.10260550, 0.02096418),
+   c(0.02096418, 0.16049956)
+ )
> 
> ## qmvnorm
> qmvnorm(p = p, tail = "lower.tail", mean = mean, sigma = sigmas,
+         interval=c(5,8))$quantile
[1] 7.020033
> qmvnorm(p = p, tail = "upper.tail", mean = mean, sigma = sigmas,
+         interval=c(-0.5,0))$quantile
[1] -0.2872104
> qmvnorm(p = p, tail = "both.tails", mean = mean, sigma = sigmas,
+         interval=c(5,8))$quantile
[1] 7.020033
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="lower.tail",df=Inf)
[1] 7.020033 7.020034
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="upper.tail",df=Inf)
[1] -0.2872110 -0.2872104
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="both.tails",df=Inf)
[1] 7.020032 7.160951
> 
> ## qmvt, shifted
> qmvt(p = p, tail = "lower.tail", delta = mean, sigma = sigmas,
+         interval=c(5,8), df=1, type="shifted")$quantile
[1] 7.214841
> qmvt(p = p, tail = "upper.tail", delta = mean, sigma = sigmas,
+         interval=c(-0.5,0), df=1, type="shifted")$quantile
[1] -0.5240962
> qmvt(p = p, tail = "both.tails", delta = mean, sigma = sigmas,
+         interval=c(5,8), df=1, type="shifted")$quantile
[1] 7.254319
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="lower.tail",
+        type="shifted",df=1)
[1] 7.191328 7.236213
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="upper.tail",
+        type="shifted",df=1)
[1] -0.5448959 -0.5014483
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="both.tails",
+        type="shifted",df=1)
[1] 7.316609 7.736290
> 
> ## qmvt, Kshirsagar
> sigmas <- cov2cor(sigmas) ## use unit variances
> qmvt(p = p, tail = "lower.tail", delta = mean, sigma = sigmas,
+         interval=c(5,8), df=1, type="Kshirsagar")$quantile
[1] 26.57861
> qmvt(p = p, tail = "upper.tail", delta = mean, sigma = sigmas,
+         interval=c(-4,0), df=1, type="Kshirsagar")$quantile
[1] -1.271525
> qmvt(p = p, tail = "both.tails", delta = mean, sigma = sigmas,
+         interval=c(5,8), df=1, type="Kshirsagar")$quantile
[1] 26.61021
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="lower.tail",
+        type="Kshirsagar",df=1)
[1]  8.126826 28.026138
> ##mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="upper.tail",
> ##       type="Kshirsagar",df=1) # will produce warnings
> mvtnorm:::getInt(p,delta=mean, sigma=sigmas,tail="both.tails",
+        type="Kshirsagar",df=1)
[1]  9.828127 29.283805
> 
> proc.time()
   user  system elapsed 
   0.70    0.03    0.73