TNorm: Truncated normal distribution

Description

Random generation for the truncated normal distribution. The mean and standard deviation of the original normal distribution are mean and sd. Truncation limits are given by a, b, type of truncation is given by trunc.

Usage

rTNorm(n, mean=0, sd=1, a, b, trunc)

Arguments

mean

mean (if common for all observations) or a vector of length n of means.

standard deviation (if common for all observations) or a vector of length n of standard deviations.

Note that mean and sd must have the same length, either 1 or n.

truncation limit 1 (if common for all observations) or a vector of length n of truncation limits 1.

truncation limit 2 (if common for all observations) or a vector of length n of truncation limits 2.

trunc

type of truncation (if common for all observations) or a vector of length n of types of truncation

[object Object],[object Object],[object Object],[object Object],[object Object]

If trunc is not given, it is assumed

number of observations to be sampled.

Value

A numeric vector with sampled values.

References

Geweke, J. (1991). Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities. Computer Sciences and Statistics, 23, 571--578.

Examples

Run this code

set.seed(1977)

### Not truncated normal distribution
x1 <- rTNorm(1000, mean=10, sd=3)
c(mean(x1), sd(x1), range(x1))

### Truncation from left only
x2 <- rTNorm(1000, mean=10, sd=3, a=7, trunc=0)
c(mean(x2), sd(x2), range(x2))

### Degenerated normal distribution
x6 <- rTNorm(1000, mean=10, sd=3, a=13, trunc=1)
c(mean(x6), sd(x6), range(x6))

### Truncation from right only
x3 <- rTNorm(1000, mean=10, sd=3, a=13, trunc=2)
c(mean(x3), sd(x3), range(x3))

### Truncation from both sides
x4 <- rTNorm(1000, mean=10, sd=3, a=7, b=13, trunc=3)
c(mean(x4), sd(x4), range(x4))

x5 <- rTNorm(1000, mean=10, sd=3, a=5.5, b=14.5, trunc=3)
c(mean(x5), sd(x5), range(x5))

oldPar <- par(mfrow=c(2, 3))
hist(x1, main="N(10, 3^2)")
hist(x2, main="TN(10, 3^2, 7, Infty)")
hist(x6, main="TN(10, 3^2, 13, 13)")
hist(x3, main="TN(10, 3^2, -Infty, 13)")
hist(x4, main="TN(10, 3^2, 7, 13)")
hist(x5, main="TN(10, 3^2, 5.5, 14.5)")
par(oldPar)

### Different truncation limits
n <- 1000
a <- rnorm(n, -2, 1)
b <- a + rgamma(n, 1, 1)
trunc <- rep(c(0, 1, 2, 3, 4), each=n/5)
x7 <- rTNorm(n, mean=1, sd=2, a=a, b=b, trunc=trunc)
cbind(trunc, a, x7)[1:10,]
sum(x7[1:(n/5)] > a[1:(n/5)])      ## must be equal to n/5

cbind(trunc, a, x7)[201:210,]
sum(x7[(n/5+1):(2*n/5)] == a[(n/5+1):(2*n/5)])         ## must be equal to n/5

cbind(trunc, x7, a)[401:410,]
sum(x7[(2*n/5+1):(3*n/5)] < a[(2*n/5+1):(3*n/5)])      ## must be equal to n/5

cbind(trunc, a, x7, b)[601:610,]
sum(x7[(3*n/5+1):(4*n/5)] > a[(3*n/5+1):(4*n/5)])      ## must be equal to n/5
sum(x7[(3*n/5+1):(4*n/5)] < b[(3*n/5+1):(4*n/5)])      ## must be equal to n/5

cbind(trunc, x7)[801:810,]

### Different moments and truncation limits
n <- 1000
mu <- rnorm(n, 1, 0.2)
sigma <- 0.5 + rgamma(n, 1, 1)
a <- rnorm(n, -2, 1)
b <- a + rgamma(n, 1, 1)
trunc <- rep(c(0, 1, 2, 3, 4), each=n/5)
x8 <- rTNorm(n, mean=1, sd=2, a=a, b=b, trunc=trunc)

### Truncation from left only
### (extreme cases when we truncate to the area
###  where the original normal distribution has
###  almost zero probability)
x2b <- rTNorm(1000, mean=0, sd=1, a=7.9, trunc=0)
c(mean(x2b), sd(x2b), range(x2b))

x2c <- rTNorm(1000, mean=1, sd=2, a=16, trunc=0)
c(mean(x2c), sd(x2c), range(x2c))

### Truncation from right only (extreme cases)
x3b <- rTNorm(1000, mean=0, sd=1, a=-7.9, trunc=2)
c(mean(x3b), sd(x3b), range(x3b))

x3c <- rTNorm(1000, mean=1, sd=2, a=-13, trunc=2)
c(mean(x3c), sd(x3c), range(x3c))

### Truncation from both sides (extreme cases)
x4b <- rTNorm(1000, mean=0, sd=1, a=-9, b=-7.9, trunc=3)
c(mean(x4b), sd(x4b), range(x4b))

x4c <- rTNorm(1000, mean=0, sd=1, a=7.9, b=9, trunc=3)
c(mean(x4c), sd(x4c), range(x4c))