Weibull distribution

Returns either the cumulative distribution or the probability density of a random variable. Used in reliability analysis, such as the calculation of the mean time to failure for a given device.

Syntax

WeibullDistribution <Cumulative> (x, Alpha, Beta)

Where:

x is the numeric value at which the distribution is evaluated.

Alpha is a distribution parameter.

Beta is a distribution parameter.

Cumulative is a logical value that determines the form of the function:

• If Cumulative = 0 (default), it returns the cumulative distribution.
• If Cumulative = 1, it returns the probability density.

Expression

For the Weibull cumulative distribution:

For the Weibull probability density:

When alpha = 1, the Weibull exponential return is

Usage Notes

The following conditions are invalid:

• alpha or beta is nonnumeric
• x < 0
• alpha < 0
• beta < 0