The Weibull distribution is a continuous probability distribution often used in reliability analysis to model time-to-failure and product lifespans.

It has applications in engineering, medicine, energy, and insurance. It’s also good at describing survival statistics, such as survival times after cancer diagnosis or electric bulb failure times. It’s used in the pharmaceutical industry to compare the in vitro dissolution profiles to establish dissolution similarity.

The two parameter Weibull distributions are characterized by a scale parameter and a shape parameter. Several methods are used to estimate the parameters and their confidence intervals. Maximum likelihood estimation (MLE) is a rigorous mathematical approach used to estimate the Weibull distribution parameters.

The pdf (probability density function) of two-parameter Weibull distribution is given by:

Equation 1

where x ≥ 0

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