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Power Normal Distribution

NIST/SEMATECH Section 1.3.6.6.13 Power Normal Distribution

PDF

PowN(p=1) PDF -4 -3 -2 -1 0 1 2 3 4 x 0 0.1 0.2 0.3 0.4 f(x)

CDF

PowN(p=1) CDF -4 -3 -2 -1 0 1 2 3 4 x 0 0.2 0.4 0.6 0.8 1 F(x)

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PDF

CDF

Formulas

Probability Density Function

f(x)=p ϕ(x)[Φ(−x)]p−1f(x) = p\,\phi(x)\left[\Phi(-x)\right]^{p-1}

Cumulative Distribution Function

F(x)=1−[Φ(−x)]pF(x) = 1 - \left[\Phi(-x)\right]^p

Properties

Mean

no closed form\text{no closed form}

Variance

no closed form\text{no closed form}

Overview

The power normal distribution is used in reliability analysis to model the minimum of pp independent normal lifetimes. When p=1p = 1 it reduces to the standard normal distribution.

Related Distributions

Normal Distribution Power Lognormal Distribution