Shifted Gompertz distribution
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The shifted Gompertz distribution is the distribution of the larger of two independent random variables one of which has an exponential distribution with parameter and the other has a Gumbel distribution with parameters and . In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution, the labelling can be considered as accurate. It has been used as a model of adoption of innovations. It was proposed by Bemmaor[1] (1994). Some of its statistical properties have been studied further by Jiménez and Jodrá [2](2009) and Jiménez Torres [3](2014).
Probability density function | |||
Cumulative distribution function | |||
Parameters |
scale (real) shape (real) | ||
---|---|---|---|
Support | |||
CDF | |||
Mean |
where and | ||
Mode |
| ||
Variance |
where and |
It has been used to predict the growth and decline of social networks and on-line services and shown to be superior to the Bass model and Weibull distribution (Bauckhage and Kersting[4] 2014).