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`stats`::`normalQuantile`

Quantile function of the normal distribution

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Syntax

```stats::normalQuantile(`m`, `v`)
```

Description

`stats::normalQuantile(m, v)` returns a procedure representing the quantile function (inverse) of the cumulative distribution function `stats::normalCDF(m, v)` of the normal distribution with mean m and variance v > 0: For 0 ≤ x ≤ 1, the solution of stats::normalCDF(m, v)(y) = x is given by y = stats::normalQuantile(m, v)(x).

The procedure `f := stats::normalQuantile(m, v)` can be called in the form `f(x)` with an arithmetical expression `x`. The return value of `f(x)` is either a floating-point number, ±`infinity`, or a symbolic expression:

If `x` is a real number between `0` and `1` and both `m` and `v` can be converted to floating-point numbers, then `f(x)` returns a real floating-point number approximating the solution `y` of ```stats::normalCDF(m, v)(y) = x```.

The calls `f(0)` and `f(0.0)` produce `-``infinity` for all values of `m` and `v`.

The calls `f(1)` and `f(1.0)` produce `infinity` for all values of `m` and `v`.

In all other cases, `f(x)` returns the symbolic call `stats::normalQuantile(m, v)(x)`.

Numerical values for m and v are only accepted if they are real and v is positive.

Environment Interactions

The function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

Examples

Example 1

We evaluate the quantile function with mean m = π and variance v = 11 at various points:

```f := stats::normalQuantile(PI, 11): f(0), f(1/10), f(0.5), f(1 - 10^(-10)), f(1)```

The value `f(x)` satisfies ```stats::normalCDF(PI, 11)(f(x)) = x```:

`stats::normalCDF(PI, 11)(f(0.987654))`

`delete f:`

Example 2

We use symbolic arguments:

`f := stats::normalQuantile(m, v): f(x), f(9/10)`

When numerical values are assigned to `m` and `v`, the function `f` starts to produce floating-point values:

`m := 17: v := 6: f(9/10), f(0.999)`

Numerical values for x are only accepted if 0 ≤ x ≤ 1:

`f(0.5)`

`f(2)`
```Error: Argument x must be between 0 and 1. [f] ```
`delete f, m, v:`

Parameters

 `m` The mean: an arithmetical expression representing a real value `v` The variance: an arithmetical expression representing a positive real value