Pedro Luiz Ramos

Exponentiated Chen distribution: Properties and estimation

ABSTRACT This article addresses various properties and estimation methods for the Exponentiated Chen distribution. Although, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, percentile estimation, least square and weighted least-square estimation, maximum product of spacings estimation, Cramér-von-Mises estimation, Anderson–Darling, and right-tail Anderson–Darling estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of three real datasets.

An Efficient, Closed-Form MAP Estimator for Nakagami-

A maximum a posteriori (MAP) estimator for the Nakagami-m fading parameter is proposed. The MAP estimator has a simple closed-form expression and can be rewritten as a bias corrected generalized moment estimator. Numerical results demonstrate that the MAP estimation scheme outperforms the existing estimation procedures and produces almost unbiased estimates for the fading parameter even for a small sample size.

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ABSTRACT The Generalized gamma (GG) distribution plays an important role in statistical analysis. For this distribution, we derive non-informative priors using formal rules, such as Jeffreys prior, maximal data information prior and reference priors. We have shown that these most popular formal rules with natural ordering of parameters, lead to priors with improper posteriors. This problem is overcome by considering a prior averaging approach discussed in Berger et al. [Overall objective priors. Bayesian Analysis. 2015;10(1):189–221]. The obtained hybrid Jeffreys-reference prior is invariant under one-to-one transformations and yields a proper posterior distribution. We obtained good frequentist properties of the proposed prior using a detailed simulation study. Finally, an analysis of the maximum annual discharge of the river Rhine at Lobith is presented.

Fading Parameter

We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments, L-moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The different estimators are compared by using extensive numerical simulations. We discovered that the maximum product of spacings estimator has the smallest mean square errors and mean relative estimates, nearest to one, for both parameters, proving to be the most efficient method compared to other methods. Combining these results with the good properties of the method such as consistency, asymptotic efficiency, normality, and invariance we conclude that the maximum product of spacings estimator is the best one for estimating the parameters of the extended exponential geometric distribution in comparison with its competitors. For the sake of illustration, we apply our proposed methodology in two important data sets, demonstrating that the EEG distribution is a simple alternative to be used for lifetime data.

Bayesian analysis of the generalized gamma distribution using non-informative priors

ABSTRACT In this study, we present different estimation procedures for the parameters of the Poisson–exponential distribution, such as the maximum likelihood, method of moments, modified moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramer–von Mises and the Anderson–Darling maximum goodness-of-fit estimators and compare them using extensive numerical simulations. We showed that the Anderson–Darling estimator is the most efficient for estimating the parameters of the proposed distribution. Our proposed methodology was also illustrated in three real data sets related to the minimum, average and the maximum flows during October at São Carlos River in Brazil demonstrating that the PE distribution is a simple alternative to be used in hydrological applications.

Different Estimation Procedures for the Parameters of the Extended Exponential Geometric Distribution for Medical Data

INTRODUCTION Measuring the impact on quality of life, especially after the beginning of the treatment, is becoming increasingly important in healthcare. OBJECTIVE The aim of this study was to translate the Chronic Otitis Media Questionnaire-12 (COMQ-12) into Portuguese language and validate this version in a group of patients with chronic otitis media. METHODS The Portuguese version of COMQ-12 was obtained by translation and back translation. Portuguese speaking patients with a history of active chronic otitis media were asked to complete the COMQ-12 Portuguese version. Cronbachs α coefficient was calculated for an estimation of the internal consistency of the questionnaire. RESULTS A total of 100 patients were included in the study; 49 women and 51 men, with a mean age of 39 years (range 12-77 years, median 40 years). The average COMQ-12 score was 29, out of a maximum score of 60. Cronbachs α result for the Portuguese version of the COMQ-12 was 0.85, indicating a high internal consistency. The participants presented with different forms of chronic otitis media, and almost all domains of the COMQ-12 questionnaire were able to differentiate between patients with healed chronic otitis media and patients with cholesteatoma or wet tympanic membrane perforation. Showing that patients with healed chronic otitis media have a better quality of life, measured by the COMQ-12, is a first step to guarantee the questionnaires validity. The next step will consist on routinely using the questionnaire in patients undergoing surgery for chronic otitis media in order to evaluate their quality of life after treatment. CONCLUSION The COMQ-12 Portuguese version showed high reliability, and may be used as an assessment of quality of life in patients with chronic otitis media.

Poisson–exponential distribution: different methods of estimation

In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.

Validation of a Portuguese version of the health-related quality of life measure for active chronic otitis media (COMQ-12)☆

ABSTRACT We discuss here an alternative approach for decreasing the bias of the closed-form estimators for the gamma distribution recently proposed by Ye and Chen in 2017. We show that, the new estimator has also closed-form expression, is positive, and can be computed for n > 2. Moreover, the corrective approach returns better estimates when compared with the former ones.

SOME COMPUTATIONAL ASPECTS TO FIND ACCURATE ESTIMATES FOR THE PARAMETERS OF THE GENERALIZED GAMMA DISTRIBUTION

In this study we considered five generalizations of the standard Weibull distribution to describe the lifetime of two important components of harvest sugarcane machines. The harvesters considered in the analysis does the harvest of an average of 20 tons of sugarcane per hour and their malfunction may lead to major losses, therefore, an effective maintenance approach is of main interesting for cost savings. For the considered distributions, the mathematical background is presented. Maximum likelihood is used for parameter estimation. Further, different discrimination procedures were used to obtain the best fit for each component. At the end, we propose a maintenance scheduling for the components of the harvesters using predictive analysis.

A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations

ABSTRACT We proposed a new class of maximum a posteriori estimators for the parameters of the Gamma distribution. These estimators have simple closed-form expressions and can be rewritten as a bias-corrected maximum likelihood estimators presented by Ye and Chen [Closed-form estimators for the gamma distribution derived from likelihood equations. Am Statist. 2017;71(2):177–181]. A simulation study was carried out to compare different estimation procedures. Numerical results revels that our new estimation scheme outperforms the existing closed-form estimators and produces extremely efficient estimates for both parameters, even for small sample sizes.