A function whose integral from A to B (with A less than or equal to B) gives the probability that a corresponding random variable assumes a value on the interval from A to B. Probabilities are given by appropriate areas under the curve representing this function.
For a continuous random variable X, the probability of X lying in a particular interval is found by integrating the p.d.f., f(x) over that interval. The p.d.f. is usually obtained by assuming a theoretical distribution for X. Note that the total area under the curve of f(x) is 1, and the function is always positive.
pdf) A mathematical model that describes the probability of events occurring over time. This function is integrated to obtain the probability that the event time takes a value in a given time interval. In life data analysis, the event in question is a failure, and the pdf is the basis for other important reliability functions, including the reliability function, the failure rate function and the mean life.