A General Purpose Approximate Goodness-of-Fit Test

“…The smaller the values of these statistics the better the fit. For more details of these statistics, see Chen and Balakrishnan (1995). We also computed the maximum values of the unrestricted and restricted log-likelihoods to obtain the likelihood ratio (LR) statistics for testing some particular cases of the EPLG distribution in Tables 3 and 5.…”

Section: Real Data Applicationsmentioning

confidence: 99%

A new four-parameter lifetime distribution

Alizadeh¹,

Bagheri

Alizadeh

et al. 2016

Journal of Applied Statistics

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Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: exponentiated power Lindley (EPL), new generalized Lindley (NGL), generalized Lindley (GL), power Lindley (PL) and Lindley geometric (LG) distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution.

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“…Further, we apply the Cramér-von Mises (W * ) and Anderson-Darling (A * ) statistics described in details in Chen and Balakrishnan (1995) to verify which distribution fits better to these data. In general, the smaller the values of the statistics W * and A * , the better the fit to the data.…”

Section: Applicationmentioning

confidence: 99%

The Exponentiated Burr XII Poisson Distribution with Application to Lifetime Data

Silva¹,

Gomes-Silva²,

Ramos³

et al. 2015

IJSP

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A five-parameter distribution, called the exponentiated Burr XII Poisson distribution, is defined and studied. The model has as special sub-models some important lifetime distributions discussed in the literature, such as the logistic, log-logistic, Weibull, Burr XII and exponentiated Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, Bonferroni and Lorenz curves, mean deviations, reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to a real data set demonstrates that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

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A General Purpose Approximate Goodness-of-Fit Test

Cited by 352 publications

References 5 publications

An Extended Burr XII Distribution: Properties, Inference and Applications

An Extended Burr XII Distribution: Properties, Inference and Applications

A new four-parameter lifetime distribution

The Exponentiated Burr XII Poisson Distribution with Application to Lifetime Data

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