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Question 1 of 10
1. Question
When the parameter 1/λ is a scale parameter in the given formula ‘X ∼ gamma(α, λ) ⇒ kX ∼ gamma(α, λ/k), for k > 0’ for the exponential distribution. The parameter α is a shape parameter – it determines the skewness and kurtosis, What happens when α increases?
Correct
When the parameter 1/λ is a scale parameter in X ∼ gamma(α, λ) ⇒ kX ∼ gamma(α, λ/k), for k > 0. The parameter α is a shape parameter – it determines the skewness and kurtosis that is why as α increases, the distribution becomes more and more symmetrical and approaches a normal distribution.
Incorrect
When the parameter 1/λ is a scale parameter in X ∼ gamma(α, λ) ⇒ kX ∼ gamma(α, λ/k), for k > 0. The parameter α is a shape parameter – it determines the skewness and kurtosis that is why as α increases, the distribution becomes more and more symmetrical and approaches a normal distribution.
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Question 2 of 10
2. Question
The Danish mathematician, statistician, and engineer A. K. Erlang gave the basics of Erlang distribution, what according to you is the best definition of it?
Correct
The Danish mathematician, statistician, and engineer A. K. Erlang gave the basics of Erlang distribution that is the gamma(α, λ) distribution when the α is an integer.
Incorrect
The Danish mathematician, statistician, and engineer A. K. Erlang gave the basics of Erlang distribution that is the gamma(α, λ) distribution when the α is an integer.
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Question 3 of 10
3. Question
The “Student’s t” family is an example of what type of family for claim distributions?
Correct
An example of a family of very thin-tailed distributions is the normal Gaussian family and an example of a family of fat-tailed distributions with
two tails is the “Student’s t” family.Incorrect
An example of a family of very thin-tailed distributions is the normal Gaussian family and an example of a family of fat-tailed distributions with
two tails is the “Student’s t” family. -
Question 4 of 10
4. Question
What is kurtosis in relation to the calculations of the distributions of the claims?
Correct
Kurtosis is known as the concept related to fat tails is a characteristic of the shape of a probability density function, which is a measure of the
“peakedness” of a density relative to that of a normal distribution.Incorrect
Kurtosis is known as the concept related to fat tails is a characteristic of the shape of a probability density function, which is a measure of the
“peakedness” of a density relative to that of a normal distribution. -
Question 5 of 10
5. Question
What is the ‘coefficient of kurtosis’ based on?
Correct
kurtosis is a measure of the “peakedness” of a density relative to that of a normal distribution. The coefficient of kurtosis is defined for distributions with finite fourth moments and is based on the fourth central moment, coded as E[(X − E[X])4].
Incorrect
kurtosis is a measure of the “peakedness” of a density relative to that of a normal distribution. The coefficient of kurtosis is defined for distributions with finite fourth moments and is based on the fourth central moment, coded as E[(X − E[X])4].
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Question 6 of 10
6. Question
Which type of values does the Pareto family allow to be realized?
Correct
The Pareto family is a wide one, with several sub-families and it is named after the Italian economist V. F. D. Pareto. It has two parameters which are denoted by α (> 0) and λ (> 0) and it allows for all positive values to be realized.
Incorrect
The Pareto family is a wide one, with several sub-families and it is named after the Italian economist V. F. D. Pareto. It has two parameters which are denoted by α (> 0) and λ (> 0) and it allows for all positive values to be realized.
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Question 7 of 10
7. Question
How many parameters does the American Pareto sub-family model for claim sizes have?
Correct
The Pareto family has a sub-division family that is used in general insurance as a model for claim sizes named as the American Pareto which has two parameters that are usually denoted α (> 0) and λ (> 0), and which allows for all positive values to be realized.
Incorrect
The Pareto family has a sub-division family that is used in general insurance as a model for claim sizes named as the American Pareto which has two parameters that are usually denoted α (> 0) and λ (> 0), and which allows for all positive values to be realized.
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Question 8 of 10
8. Question
Which out of these is a benefit of mixture distributions?
Correct
Mixture distributions enable to include the variability amongst risks in a portfolio which is also known as modeling of heterogeneity of risks, it provides a source of fat-tailed loss distributions, and finally, it sheds further light on some distributions already dealt with.
Incorrect
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Question 9 of 10
9. Question
Which type of method of parameter estimation is known to be very poor and unreliable?
Correct
Method of Moments is relatively easy to implement, but the estimates it produces tend to have high standard errors, making it very poor and unreliable.
Incorrect
Method of Moments is relatively easy to implement, but the estimates it produces tend to have high standard errors, making it very poor and unreliable.
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Question 10 of 10
10. Question
Why is the Burr distribution is called as “transformed Pareto” distribution?
Correct
The Pareto family is known to be the two-parameter sub-family for the case τ = 1. Whereas The Burr random variable is obtainable as a power function of a Pareto random variable – if X ∼ Pa(α, λ) then Y = X1/τ ∼ Burr(α, λ, τ), or, equivalently, if X ∼ Burr(α, λ, τ) then Xτ ∼ Pa(α, λ). That is why the Burr distribution is called as “transformed Pareto” distribution.
Incorrect
The Pareto family is known to be the two-parameter sub-family for the case τ = 1. Whereas The Burr random variable is obtainable as a power function of a Pareto random variable – if X ∼ Pa(α, λ) then Y = X1/τ ∼ Burr(α, λ, τ), or, equivalently, if X ∼ Burr(α, λ, τ) then Xτ ∼ Pa(α, λ). That is why the Burr distribution is called as “transformed Pareto” distribution.