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Quantile function of the exponential distribution

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stats::exponentialQuantile(a, b)


stats::exponentialQuantile(a, b) returns a procedure representing the quantile function (inverse)

of the cumulative distribution function stats::exponentialCDF(a, b). For 0 ≤ x ≤ 1, the solution of stats::exponentialCDF(a, b)(y) = x is given by


The procedure f := stats::exponentialQuantile(a, b) 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 floating-point number between 0 and 1 and a and b can be converted to suitable real floating-point numbers, then f(x) returns a floating-point number.

The calls f(1) and f(1.0) produce infinity.

In all other cases, f(x) returns the symbolic expression a-ln(1-x)/b.

Numerical values of x are only accepted if 0 ≤ x ≤ 1.

Numerical values of a and b are only accepted if they are real and b is positive.

Environment Interactions

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


Example 1

We evaluate the quantile function with a = 2 and b = 3 at various points:

f := stats::exponentialQuantile(2, 3):
f(0), f(1/10), f(0.5), f(1 - 10^(-10)), f(1)

The value f(x) satisfies stats::exponentialCDF(2, 3)(f(x)) = x:

stats::exponentialCDF(2, 3)(f(0.987654))

delete f:

Example 2

We use symbolic arguments:

f := stats::exponentialQuantile(a, b): f(x), f(1/3), f(0.4)

When suitable numerical values are assigned to a and b, the function f starts to produce numerical values:

a := 7: b := 1/8: f(0.999), f(999/1000)

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


Error: An argument x with 0 <= x <= 1 is expected. [f]
delete f, a, b:



The location parameter: an arithmetical expression representing a real value


The scale parameter: an arithmetical expression representing a positive real value

Return Values


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