The Gompertz distribution is a continuous probability distribution often used to model the time until an event occurs, particularly in survival analysis and reliability engineering. It is characterized by a cumulative distribution function (CDF) that describes the likelihood of the time until an event, such as failure or death, occurs.
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A positive, exponentially increasing hazard function gives the survivor functionIts mean is , where is the exponential integral. Unlike the exponential distribution, its future mean waiting time is not the reciprocal of its current hazard function.