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Answer: The power law specifies the probability of observing a value greater than a given value.
D is correct. Power law tails provide the probability of seeing a realization larger than a given/specified value of x. A is incorrect. The Student's t is an example of a widely used distribution with a power law tail. Normal distributions have thin tails, while power law tails create non-normal distributions. B is incorrect. As stated in A, the Student's t is a valid example of a distribution that exhibits a power law tail. C is incorrect. The slow decline in the probability of observing large values is a trait that is observed in fat-tailed distributions, not in thin-tailed distributions such as that of the normal distribution.
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A senior analyst at a financial firm is conducting a presentation for junior analysts on the characteristics and applications of the power law. The focus is on understanding the importance of the power law in analyzing the tails, or extremities, of distribution curves in financial data. Which statement accurately describes the power law?
A
Power law tails are only observed in normal distributions.
B
Power law tails are not present in the Student's t distribution.
C
The power law models the slow decline in the probability of observing large values in thin-tailed distributions.
D
The power law specifies the probability of observing a value greater than a given value.
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