
Explanation:
The Generalized Extreme Value (GEV) distribution becomes the Frechet distribution when the shape parameter is greater than zero. The Frechet distribution is a particular case of the GEV distribution and is used to model the distribution of extreme events. It is named after the French mathematician Maurice Fréchet and is a type of extreme value distribution. The Frechet distribution is heavy-tailed and is appropriate for modeling the maximum values of distributions with a heavy right tail. This means it is often used in fields such as hydrology, telecommunications, finance, and insurance to model extreme events such as large floods, large insurance claims, or large stock market movements. The Frechet distribution applies when the cumulative distribution of obeys a power function, indicating that it is heavy-tailed. This is why when , the GEV becomes the Frechet distribution.
Choice B is incorrect. The Pareto distribution is a power-law probability distribution, which does not morph from the GEV distribution when the shape parameter is greater than zero. It has its own set of parameters and characteristics that are distinct from those of the GEV.
Choice C is incorrect. The Gumbel distribution, also known as type I extreme value distribution, corresponds to a case where the shape parameter equals zero in the GEV family of distributions. Therefore, it cannot be obtained when is greater than zero.
Choice D is incorrect. Similar to Gumbel, Weibull or type III extreme value distributions correspond to a scenario where the shape parameter in the GEV family of distributions is less than zero and not greater than zero.
Ultimate access to all questions.
Q.2179 The following is the probability distribution function of the generalized extreme value distribution:
Where satisfies the condition $1 + \dfrac{\xi(X - \mu)}{\sigma} > 0$
If , the GEV becomes the:
A
Frechet distribution
B
Pareto distribution
C
Gumbel distribution
D
Weibull distribution
No comments yet.