RiskWeibull

Description

RiskWeibull specifies a Weibull distribution with shape parameter and scale parameter . This distribution is often used in reliability studies to model the lifetime of a device. When is greater than 1, the usual case, the distribution has the “wearout” property where the older the device is, the more likely it is to fail in the near future. The opposite is true when is less than 1, which usually makes this parameter value unrealistic. When equals 1, this distribution is equivalent to an exponential distribution, with a constant failure rate.

Examples

RiskWeibull(3,20) returns a Weibull distribution with shape parameter 3 and scale parameter 20.

RiskWeibull(D1,D2) generates a Weibull distribution with shape parameter taken from cell D1 and scale parameter taken from cell D2.

Guidelines

Both and must be positive.

Parameters

     continuous shape parameter      

     continuous scale parameter      

Domain

     continuous

Density and Cumulative Distribution Functions

Mean

Here, Γ is the Gamma Function.

Variance

Skewness

Kurtosis

Mode

          for

0           for

Examples