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stats::binomialQuantile

Quantile function of the binomial distribution

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Syntax

stats::binomialQuantile(n, p)

Description

stats::binomialQuantile(n, p) returns a procedure representing the quantile function (discrete inverse) of the cumulative distribution function stats::binomialCDF(n, p). For 0 ≤ x ≤ 1, the quantile value k = stats::binomialQuantile(n, p)(x) satisfies

.

The procedure f := stats::binomialQuantile(n, p) can be called in the form f(x) with arithmetical expressions x. The return value of f(x) is either a natural number between 0 and n, or a symbolic expression:

  • If n is a positive integer, p a real number satisfying 0 ≤ p ≤ 1, and x a real number satisfying 0 ≤ x ≤ 1, then f(x) returns an integer between 0 and n.

  • If p = 0, then f(x) returns 0 for any values of n and x.

  • If p = 1, then f(x) returns n for any values of n and x.

  • For p ≠ 1, the call f(0) returns 0 for any value of n.

  • For p ≠ 0, the call f(1) returns n for any value of n.

  • In all other cases, f(x) returns the symbolic call stats::binomialQuantile(n, p)(x).

Numerical values for n are only accepted if they are positive integers.

Numerical values for p are only accepted if they satisfy 0 ≤ p ≤ 1.

If floating-point arguments are passed to the quantile function f, the result is computed with floating-point arithmetic. This is faster than using exact arithmetic, but the result is subject to internal round-off errors. In particular, round-off may be significant for arguments x close to 1. Cf. Example 3.

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 n = 30 and at some points:

f := stats::binomialQuantile(30, 1/3): 
f(0), f((2/3)^30), f(PI/10), f(0.5), f(1 - 1/10^10)

The quantile value f(x) satisfies

:

x := 0.7: f(x)

stats::binomialCDF(30, 1/3)(float(f(x) - 1)), x,
stats::binomialCDF(30, 1/3)(float(f(x)))

delete f, x:

Example 2

We use symbolic arguments:

f := stats::binomialQuantile(n, p): f(x), f(9/10)

When n and p evaluate to suitable numbers, the function f starts to produce quantile values:

n := 80: p := 1/10:
f(1/2),  f(999/1000), f(1 - 1/10^10), f(1 - 1/10^80)

delete f, n, p:

Example 3

If floating-point arguments are passed to the quantile function, the result is computed with floating-point arithmetic. This is faster than using exact arithmetic, but the result is subject to internal round-off errors:

f := stats::binomialQuantile(1000, 1/30): 
f(1 - 1/10^16) <> f(float(1 - 1/10^16))

delete f:

Parameters

n

The "trial parameter": an arithmetical expression representing a positive integer

p

The "probability parameter": an arithmetical expression representing a real number 0 ≤ p ≤ 1.

Return Values

procedure.

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