General treatment of goodness-of-fit tests based on Kullback–Leibler information

2015

Ann. Data. Sci.

Direct integration of the Riemann-Stieltjes integral has been used to computing convolution integrals. This approach has been established to be simple and accurate with good convergence property. In this paper, we used some numerical methods to estimation of entropy of a continuous random variable and then some estimators are introduced. Bounds on the error terms are derived for some direct Riemann-Stieltjes integration methods. Consistency of estimators is proved and by simulation, the proposed estimators are compared with some prominent estimators,

“…Entropy estimators are used to developing entropy-based statistical procedures. See for example, [1,2,10,13,20,21]. Therefore, new entropy estimators can be useful in practice.…”

Section: Hv Mnmentioning

confidence: 99%

Entropy Estimation Using Numerical Methods

2015

Ann. Data. Sci.

“…So, an estimate of KL information has been used as a test statistic for goodness of fit purposes. For example, Arizono and Ohta [12], Ebrahimi et al [13], Park and Park [14], and Alizadeh Noughabi and Arghami [15] have discussed such tests for complete samples, while Balakrishnan et al [10], Lim and Park [16], Lin et al [17], Castro-Kuriss [18], Habibi Rad et al [19], Grané [20], Pakyari and Balakrishnan [21], and Park and Lim [22] developed tests based on censored samples. Moreover, Ebrahimi [23] considered the problem of testing the goodness of fit for the exponentiality of the remaining life of a system at a certain age.…”

Section: Introductionmentioning

confidence: 99%

Goodness of Fit Using a New Estimate of Kullback-Leibler Information Based on Type II Censored Data

2015

IEEE Trans. Rel.

In this article, a general goodness of fit test is developed by using a new estimate of Kullback-Leibler (KL) information based on Type-II censored data. The proposed test is consistent, and the test statistic is nonnegative, just like KL information. Then, the test statistic is used to test for exponentiality based on Type-II censored data. Through a simulation study, power values of the proposed test are compared with some prominent existing tests. A real-life data analysis is finally presented for illustrative purpose.

“…Therefore, such a distributional assumption must be checked carefully. This problem has been discussed by many authors in the form of goodness of fit tests; see, for example [1,2,11,19,20,23,30,32,34,37,38].…”

Section: Introductionmentioning

confidence: 99%

Tests of goodness of fit based on Phi-divergence

Journal of Applied Statistics

2015

In this paper, we introduce a general goodness of fit test based on Phi-divergence. Consistency of the proposed test is established. We then study some special cases of tests for normal, exponential, uniform and Laplace distributions. Through Monte Carlo simulations, the power values of the proposed tests are compared with some known competing tests under various alternatives. Finally, some numerical examples are presented to illustrate the proposed procedure.