Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

Noughabi, Hadi Alizadeh

doi:10.1007/s40745-015-0041-0

Cited by 7 publications

(8 citation statements)

References 22 publications

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“…The tests generally fail to achieve the specified nominal significance level of 5% against the P(1, 1) distribution. Of course, the tests for which parameter estimation are not required (T n , I n2,2 , I n,3 , I [1] n and I [2] n ) do not exhibit this shortcoming. The general lack of adherence to the specified significance level can be ascribed to the fact that the first moment of the P(1, 1) distribution does not exist.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…As with the tests given in Section 2.8.3, Obradović [39] concludes that, while neither of the tests was dominant against all alternatives in terms of local efficiency, they are both locally optimal for certain classes of alternatives. It is again showed that I [2] n has an asymptotic normally distributed null distribution.…”

Section: Characterisation 4 [39]mentioning

confidence: 91%

“…All three of these tests reject the null hypothesis for large values of the test statistics. Building on the tests for the assumption of normality that Zhang [54] proposes, Alizadeh Noughabi [2] adapts two of these test to test the assumption of exponentiality. Neither Zhang [54] nor Alizadeh Noughabi [2] derive the asymptotic properties of these tests and rather present extensive Monte Carlo studies to investigate their finite sample performances.…”

Section: Tests Based On Likelihood Ratiosmentioning

confidence: 99%

“…Building on the tests for the assumption of normality that Zhang [54] proposes, Alizadeh Noughabi [2] adapts two of these test to test the assumption of exponentiality. Neither Zhang [54] nor Alizadeh Noughabi [2] derive the asymptotic properties of these tests and rather present extensive Monte Carlo studies to investigate their finite sample performances. The authors found that these tests are quite powerful compared to other tests (especially the traditional edf-based tests) against a range of alternatives.…”

Section: Tests Based On Likelihood Ratiosmentioning

confidence: 99%

“…positive absolutely continuous random variables with strictly monotone distribution function and monotonically increasing or decreasing hazard function and denote the order statistics by X (1) ≤ X (2) ≤ X (3) . The random variable X (3) /X (2) and X (2) /X (1) have the same distribution if, and only if, the distribution of X follows a Pareto distribution.…”

Section: Characterisation 4 [39]mentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Simulation Results and Discussionmentioning

confidence: 99%

Section: Characterisation 4 [39]mentioning

confidence: 91%

Section: Tests Based On Likelihood Ratiosmentioning

confidence: 99%

Section: Tests Based On Likelihood Ratiosmentioning

confidence: 99%

Section: Characterisation 4 [39]mentioning

confidence: 99%

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Testing for the Pareto type I distribution: a comparative study

Santana

et al. 2023

METRON

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Probability Distributions and Their Applications

Maity

2018

Springer Transactions in Civil and Environmental Engineering

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An ‘apples to apples’ comparison of various tests for exponentiality

et al. 2017

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The exponential distribution is a popular model both in practice and in theoretical work. As a result, a multitude of tests based on varied characterisations have been developed for testing the hypothesis that observed data are realised from this distribution. Many of the recently developed tests contain a tuning parameter, usually appearing in a weight function. In this paper we compare the powers of 20 tests for exponentiality-some containing a tuning parameter and some that do not. To ensure a fair 'apples to apples' comparison between each of the tests, we employ a data-dependent choice of the tuning parameter for those tests that contain these parameters. The comparisons are conducted for various samples sizes and for a large number of alternative distributions. The results of the simulation study show that the test with the best overall power performance is the Baringhaus & Henze test, followed closely by the test by Henze & Meintanis; both tests contain a tuning parameter. The score test by Cox & Oakes performs the best among those tests that do not include a tuning parameter.

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Testing Exponentiality Based on the Likelihood Ratio and Power Comparison

Cited by 7 publications

References 22 publications

Testing for the Pareto type I distribution: a comparative study

Testing for the Pareto type I distribution: a comparative study

Probability Distributions and Their Applications

An ‘apples to apples’ comparison of various tests for exponentiality

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