dpnorm | R Documentation |

Evaluates the difference between two `N(0,1)`

cumulative distribution functions avoiding cancellation error.

```
dpnorm(x0,x1)
```

`x0` |
vector of lower values at which to evaluate standard normal distribution function. |

`x1` |
vector of upper values at which to evaluate standard normal distribution function. |

Equivalent to `pnorm(x1)-pnorm(x0)`

, but stable when `x0`

and `x1`

values are very close, or in the upper tail of the standard normal.

Simon N. Wood simon.wood@r-project.org

```
require(mgcv)
x <- seq(-10,10,length=10000)
eps <- 1e-10
y0 <- pnorm(x+eps)-pnorm(x) ## cancellation prone
y1 <- dpnorm(x,x+eps) ## stable
## illustrate stable computation in black, and
## cancellation prone in red...
par(mfrow=c(1,2),mar=c(4,4,1,1))
plot(log(y1),log(y0),type="l")
lines(log(y1[x>0]),log(y0[x>0]),col=2)
plot(x,log(y1),type="l")
lines(x,log(y0),col=2)
```

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