Discriminating between gamma and lognormal distributions with applications

Alzaid, Abdulhamid A.

doi:10.1016/j.jksus.2009.07.003

Cited by 6 publications

(3 citation statements)

References 31 publications

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“…The data given arose in tests on endurance of deep groove ball bearings. The data are number of million revolutions before failure for each of the lifetime tests and they are: 17 Here we consider Gamma model as the component of vector of densities F θ and log-normal as the component of F γ defined respectively in section 7. Therefore, to analyze a skewed positive data set an experimenter might wish to select one of them.…”

Section: Example With Real Datamentioning

confidence: 99%

Discriminating between two models based on Bregman divergence in small samples

Ngom¹,

Nkurunziza²,

Ogouyandjou³

2017

Preprint

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Recently in [1,2], Ali-Akbar Bromideh introduced the Kullback-Leibler Divergence (KLD) test statistic in discriminating between two models. It was found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better than the Ratio of Maximized Likelihood (RML) for small sample size. The aim of this paper is to generalize the works of Ali-Akbar Bromideh by proposing a hypothesis testing based on Bregman divergence in order to improve the process of choice of the model. Our aproach differs from him. After observing n data points of unknown density f ; we firstly measure the closness between the bias reduced kernel density estimator and the first estimated candidate model. Secondly between the bias reduced kernel density estimator and the second estimated candidate model. In these two cases Bregman Divergence (BD) and the bias reduced kernel estimator [3] focuses on improving the convergence rates of kernel density estimators are used. Our testing procedure for model selection is thus based on the comparison of the value of model selection test statistic to critical values from a standard normal table. We establish the asymptotic properties of Bregman divergence estimator and approximations of the power functions are deduced. The multi-step MLE process will be used to estimate the parameters of the models. We explain the applicability of the BD by a real data set and by the data generating process (DGP). The Monte Carlo simulation and then the numerical analysis will be used to interpret the result.

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Section: Example With Real Datamentioning

confidence: 99%

Discriminating between two models based on Bregman divergence in small samples

Ngom¹,

Nkurunziza²,

Ogouyandjou³

2017

Preprint

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“…There are a lot of works in this area. Some of them are Alzaid & Sultan [1], Kundu & Manglick [2], Bromideh and Valizadeh [3], Dey and Kundu [4], Dey and Kundu [5], Kundu [6], Kantam et al [7], Ngom, et al [8], Ravikumar and Kantam,[9], Qaffou and Zoglat, [10] and Algamal [11].…”

Section: Introductionmentioning

confidence: 99%

Discriminating between the Lognormal and Weibull Distributions under Progressive Censoring

Kuş¹,

Pekgör²,

Kınacı³

2019

Cumhuriyet Science Journal

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In this paper, the ratio of maximized likelihood and Minimized Kullback-Leibler Divergence methods are discussed for discrimination between log-normal and Weibull distributions. The progressive Type-II right censored sample is considered in the study. The probability of correct selections is simulated and compared to investigate the performance of the procedures for different censoring schemes and parameter settings.

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“…Considering a candidate model for some given data generated by an unknown probability distribution, the dissimilarity between those two probability distributions can be measured by the Kullback-Leibler divergence (KLD) introduced by Kullback and Leibler [9]. Since the true density is unknown, various criteria and hypothesis testing were used for model selection purpose ( [10,11,12,13,14,15,16,17,18]). In this paper, we shall derive a strongly consistent estimator of KLD between two distributions based on the bais reduced kernel density estimator.…”

Section: Introductionmentioning

confidence: 99%