Tests of goodness of fit based on Phi-divergence

Noughabi, Hadi Alizadeh

doi:10.1080/02664763.2015.1063116

Cited by 11 publications

(4 citation statements)

References 33 publications

(27 reference statements)

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“…Lastly, the critical values used in Chu et al [16] are obtained using a bootstrap approach; in Sect. 3, we show that it is possible to obtain critical values independent of the estimated parameters when using maximum likelihood estimation. This allows us to estimate critical values without resorting to a bootstrap procedure in the case where maximum likelihood parameter estimates are employed.…”

Section: Introductionmentioning

confidence: 91%

“…In addition to showing that the tests above are consistent against fixed alternatives (no derivation of the asymptotic null distribution was presented), Alizadeh Noughabi & Balakrishnan [3] also uses DK n , D H n , D J n and DT n to test the goodness-of-fit hypothesis for the normal, exponential, uniform and Laplace distributions. The Monte Carlo study included in Alizadeh Noughabi & Balakrishnan [3] indicates that DK n produces the highest powers amongst the phi-divergence type tests. When comparing the performance of these tests, the powers associated with DK n were higher than the others.…”

Section: Tests Based On the Phi-divergencementioning

confidence: 99%

“…Obradović [39] uses the following special case of Rossberg's characterisation of the Pareto distribution to construct a goodness-of-fit test: Let X 1 , X 2 , and X 3 be i.i.d. positive absolutely continuous random variables and denote the corresponding order statistics by X (1) ≤ X (2) ≤ X (3) . If X (2) /X (1) and min(X 1 , X 2 ) are identically distributed, then X 1 follows a Pareto distribution.…”

Section: Characterisation 3 [46]mentioning

confidence: 99%

“…Let X 1 , X 2 and X 3 be i.i.d. 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%

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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: Introductionmentioning

confidence: 91%

Section: Tests Based On the Phi-divergencementioning

confidence: 99%