Shifted Gompertz distribution
|Probability density function
|Cumulative distribution function
|Parameters|| scale (real)
The shifted Gompertz distribution is the distribution of the largest of two independent random variables one of which has an exponential distribution with parameter b and the other has a Gumbel distribution with parameters and b. 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 (truncated at zero), the labelling can be considered as accurate. It has been used as a model of adoption of innovations. It was proposed by Bemmaor (1994).
The probability density function of the shifted Gompertz distribution is:
The cumulative distribution function of the shifted Gompertz distribution is:
The shifted Gompertz distribution is right-skewed for all values of . It is more flexible than the Gumbel distribution.
The shifted Gompertz density function can take on different shapes depending on the values of the shape parameter :
- the probability density function has its mode at 0.
- the probability density function has its mode at
- where is the smallest root of
- which is
If varies according to a gamma distribution with shape parameter and scale parameter (mean = ), the distribution of is Gamma/Shifted Gompertz (G/SG). When is equal to one, the G/SG reduces to the Bass model.
- Gumbel distribution
- Generalized extreme value distribution
- Mixture model
- Bass model
- Gompertz distribution
||This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (April 2012)|
- Bemmaor, Albert C. (1994). "Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity". In G. Laurent, G.L. Lilien & B. Pras. Research Traditions in Marketing. Boston: Kluwer Academic Publishers. pp. 201–223. ISBN 0-7923-9388-0.
- Chandrasekaran, Deepa; Tellis, Gerard J. (2007). "A Critical Review of Marketing Research on Diffusion of New Products". In Naresh K. Malhotra. Review of Marketing Research 3. Armonk: M.E. Sharpe. pp. 39–80. ISBN 978-0-7656-1306-6.
- Dover, Yaniv; Goldenberg, Jacob; Shapira, Daniel (2012). "Network Traces on Penetration: Uncovering Degree Distribution From Adoption Data". Marketing Science. doi:10.1287/mksc.1120.0711.
- Jimenez, Fernando; Jodra, Pedro (2009). "A Note on the Moments and Computer Generation of the Shifted Gompertz Distribution". Communications in Statistics - Theory and Methods 38 (1): 78–89. doi:10.1080/03610920802155502.
- Van den Bulte, Christophe; Stremersch, Stefan (2004). "Social Contagion and Income Heterogeneity in New Product Diffusion: A Meta-Analytic Test". Marketing Science 23 (4): 530–544. doi:10.1287/mksc.1040.0054.
Content from Wikipedia, the Free Encyclopedia
What Is This Site? The Ultimate Study Guide is a mirror of English Wikipedia. It exists in order to provide Wikipedia content to those who are unable to access the main Wikipedia site due to draconian government, employer, or school restrictions. The site displays all the text content from Wikipedia. Our sponsors generously cover part of the cost of hosting this site, and their ads are shown as part of this agreement. We regret that we are unable to display certain controversial images on some pages the site at the request of the sponsors. If you need to see images which we are unable to show, we encourage you to view Wikipedia directly if possible, and apologize for this inconvenience.
A product of XPR Content Systems. 47 Union St #9K, Grand Falls-Windsor NL A2A 2C9 CANADA