Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization

Allison, James S.; Milošević, Bojana; Obradović, M; Smuts, Marius

doi:10.1007/s00180-021-01126-y

Cited by 11 publications

(9 citation statements)

References 28 publications

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“…The proposed tests are based on a characterisation of the Pareto distribution via the distribution of the sample minimum. This characterisation is discussed in Allison et al (2022) and is as follows:…”

Section: A New Class Of Tests For the Pareto Distributionmentioning

confidence: 99%

On a new class of tests for the Pareto distribution using Fourier methods

L.¹,

S.²,

Smuts³

et al. 2023

Preprint

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We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are U and V statistics based on a characterisation of the Pareto distribution involving the distribution of the sample minimum. In addition to deriving simple computational forms for the proposed test statistics, we prove consistency against a wide range of fixed alternatives. A Monte Carlo study is included in which the newly proposed tests are shown to produce high powers. These powers include results relating to fixed alternatives as well as local powers against mixture distributions. The use of the proposed tests is illustrated using an observed data set.

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Section: A New Class Of Tests For the Pareto Distributionmentioning

confidence: 99%

On a new class of tests for the Pareto distribution using Fourier methods

L.¹,

S.²,

Smuts³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The proposed tests are based on a characterization of the Pareto distribution via the distribution of the sample minimum. This characterization is discussed in Allison et al (2022) and is as follows:…”

Section: A New Class Of Tests For the Pareto Distributionmentioning

confidence: 99%

“…• A test proposed by Allison et al (2022), which is also based on the characterization given in Theorem 1, but makes use of empirical distribution functions instead of empirical characteristic functions. The test statistic is given by…”

Section: Monte Carlo Studymentioning

confidence: 99%

On a new class of tests for the Pareto distribution using Fourier methods

Allison

Smuts

et al. 2023

Stat

Self Cite

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We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are and statistics based on a characterization of the Pareto distribution involving the distribution of the sample minimum. In addition to deriving simple computational forms for the proposed test statistics, we prove consistency against a wide range of fixed alternatives. A Monte Carlo study is included in which the newly proposed tests are shown to produce high powers. These powers include results relating to fixed alternatives as well as local powers against mixture distributions. The use of the proposed tests is illustrated using an observed data set.

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“…Using m as a tuning parameter, Allison et al [6] proposes three classes of tests for the Pareto distribution based on the characterisation above. The test statistics used are discrepancy measures between the empirical distribution of min{X 1 , ..., X m } and the V -empirical distribution of m √ X , defined as…”

Section: Characterisation 2 [6]mentioning

confidence: 99%

“…K n,m and M n,m reject the null hypothesis for large values of the test statistics, while I n,m rejects for large values of |I n,m |. Allison et al [6] derive the limiting null distribution of all three test statistics. Upon calculating and comparing the Bahadur efficiencies, Allison et al [6] found that the test I n,m has the best performance among the three in terms of local efficiency.…”

Section: Characterisation 2 [6]mentioning

confidence: 99%

Testing for the Pareto type I distribution: a comparative study

Santana

et al. 2023

METRON

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Pareto distributions are widely used models in economics, finance and actuarial sciences. As a result, a number of goodness-of-fit tests have been proposed for these distributions in the literature. We provide an overview of the existing tests for the Pareto distribution, focussing specifically on the Pareto type I distribution. To date, only a single overview paper on goodness-of-fit testing for Pareto distributions has been published. However, the mentioned paper has a much wider scope than is the case for the current paper as it covers multiple types of Pareto distributions. The current paper differs in a number of respects. First, the narrower focus on the Pareto type I distribution allows a larger number of tests to be included. Second, the current paper is concerned with composite hypotheses compared to the simple hypotheses (specifying the parameters of the Pareto distribution in question) considered in the mentioned overview. Third, the sample sizes considered in the two papers differ substantially. In addition, we consider two different methods of fitting the Pareto Type I distribution; the method of maximum likelihood and a method closely related to moment matching. It is demonstrated that the method of estimation has a profound effect, not only on the powers achieved by the various tests, but also on the way in which numerical critical values are calculated. We show that, when using maximum likelihood, the resulting critical values are shape invariant and can be obtained using a Monte Carlo procedure. This is not the case when moment matching is employed. The paper includes an extensive Monte Carlo power study. Based on the results obtained, we recommend the use of a test based on the phi divergence together with maximum likelihood estimation.

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Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization

Cited by 11 publications

References 28 publications

On a new class of tests for the Pareto distribution using Fourier methods

On a new class of tests for the Pareto distribution using Fourier methods

On a new class of tests for the Pareto distribution using Fourier methods

Testing for the Pareto type I distribution: a comparative study

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