Weibull Distribution (Two Parameter)

The Weibull distribution is a special case of the Generalized Extreme Value distribution.  It has been extensively used as a model of time to failure of manufactured items and has become one of the principal tools of reliability engineering.  The applications of the Weibull distribution have expanded and include finance and climatology.

The distribution is named after the Swedish engineer Wallodi Weibull.

Profile

Parameters

Parameter	Description	Characteristics
scale	defines the range and practical maximum.  Also known as the characteristic life.	A float > -∞ and < ∞
shape	Determines the profile of the distribution.	A float > 0

Range

The range is from greater than zero to positive infinity.  However, in practice the right tail is classed as thin/light or bounded.

Functions

Properties

Random Number Generation

Random number generation (referred to as r) for a Weibull distribution can be performed by transforming a continuous uniform variable in the range 0 to 1 (referred to as u) with the distribution's inverse probability function:

r=g(u)

Using Basic style code, the function would be similar to:

r = scale * (log(1 / rnd)) ^ (1 / shape)

Page Updated: 05-May-2005

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