Statistical distributions have been formulated by statisticians, mathematicians and engineers to mathematically model or represent certain behavior. The probability density function (pdf) is a mathematical function that describes the distribution. The pdf can be represented mathematically or on a plot where the x-axis represents time, as shown next.
Graphic demonstration of the probability density function (pdf)
The equation below gives the pdf for the 3-parameter Weibull distribution. Some distributions, such as the Weibull and lognormal, tend to better represent life data and are commonly called "lifetime distributions" or "life distributions." In fact, life data analysis is sometimes called "Weibull analysis" because the Weibull distribution, formulated by Professor Waloddi Weibull, is a popular distribution for analyzing life data. The Weibull model can be applied in a variety of forms (including 1-parameter, 2-parameter, 3-parameter or mixed Weibull). Other commonly used life distributions include the exponential, lognormal and normal distributions. The analyst chooses the life distribution that is most appropriate to model each particular data set based on past experience and goodness-of-fit tests.
3-parameter Weibull distribution probability density function (pdf)