Quantile function of the normal distribution
MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.
MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.
stats::normalQuantile(m
, v
)
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 floatingpoint 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 floatingpoint numbers, then f(x)
returns a
real floatingpoint 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.
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision.
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:
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 floatingpoint
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: An argument x with 0 <= x <= 1 is expected. [f]
delete f, m, v:

The mean: an arithmetical expression representing a real value 

The variance: an arithmetical expression representing a positive real value 