pystats_norm.qnorm

Functions

qnorm(p[, mean, sd, lower_tail])

Quantile (Inverse Cumulative Distribution Function) of the normal distribution.

Module Contents

pystats_norm.qnorm.qnorm(p, mean=0, sd=1, lower_tail=True)[source]

Quantile (Inverse Cumulative Distribution Function) of the normal distribution.

Parameters:

  • p (np.float64) – The probability for which to find the quantile. Must be between 0 and 1 (exclusive).

  • mean (np.float64, optional) – The mean (average) of the normal distribution. Default is 0.

  • sd (np.float64, optional) – The standard deviation of the normal distribution. Default is 1.

  • lower_tail (bool, optional) – If True, return the probability to the left of p in the normal distribution. If False, return the probability to the right of p in the normal distribution. Default is True.

Returns:

  • np.float64 – Returns the value of the inverse cumulative density function (cdf) of the normal distribution given a certain random variable p, a population mean μ, and the population standard deviation σ.

  • Formula

  • ——-

  • If lower_tail=True – Q(p; μ, σ) = μ + σ * sqrt(2) * erfinv(2p - 1)

  • If lower_tail=False – Q(p; μ, σ) = μ - σ * sqrt(2) * erfinv(2p - 1)

  • The quantile represents the value below which a given proportion of the distribution

  • falls. It is characterized by the mean (μ) and standard deviation (σ), determining

  • the center and spread of the distribution.

Example

>>> qnorm(0.8413447460685429, mean=0, sd=1, lower_tail=True)
1.0