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Kalkulator odwrotnego rozkładu normalnego (kwantyl)

Znajdź wartość odpowiadającą danemu skumulowanemu prawdopodobieństwu normalnemu.

Wprowadzenie

Normal Inverse (Quantile) Calculator — Find the value corresponding to a given normal cumulative probability. Enter Probability (0-1), Mean (μ), Std. deviation (σ) to get an instant, accurate result.

Wzór

Given a cumulative probability p, finds the value x such that P(X ≤ x) = p, using Peter Acklam's rational approximation of the inverse standard normal CDF (the quantile function), then scaling by mean + z×σ. This is a numerical approximation, since no closed-form inverse exists.

Krok po kroku

  1. Enter the Probability (0-1).
  2. Enter the Mean (μ).
  3. Enter the Std. deviation (σ).
  4. Click Calculate to see your result instantly.

Przykład z życia

Example: With Probability (0-1) = 0.975, Mean (μ) = 0, Std. deviation (σ) = 1, the Normal Inverse (Quantile) Calculator gives Z Or X: 1.96.

Często Zadawane Pytania

What is this also called?
It's the quantile function, sometimes called the inverse normal or probit function — the opposite operation of the normal CDF.
What values of p are valid?
p must be strictly between 0 and 1; at exactly 0 or 1 the corresponding value would be negative or positive infinity.
What inputs does the Normal Inverse (Quantile) Calculator need?
You'll need to provide: Probability (0-1), Mean (μ), Std. deviation (σ). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Normal Inverse (Quantile) Calculator?
The Normal Inverse (Quantile) Calculator applies the formula exactly as calculated — Given a cumulative probability p, finds the value x such that P(X ≤ x) = p, using Peter Acklam's rational approximation of the inverse standard normal CDF (the quantile function), then scaling by mean + z×σ. This is a numerical approximation, since no closed-form inverse exists. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Normal Inverse (Quantile) Calculator free to use?
Yes, the Normal Inverse (Quantile) Calculator is completely free, requires no signup, and runs instantly in your browser.

O Kalkulator odwrotnego rozkładu normalnego (kwantyl)

The Normal Inverse (Quantile) Calculator uses a real, verifiable formula — Given a cumulative probability p, finds the value x such that P(X ≤ x) = p, using Peter Acklam's rational approximation of the inverse standard normal CDF (the quantile function), then scaling by mean + z×σ. This is a numerical approximation, since no closed-form inverse exists. — so results are accurate every time, not an approximation.