Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data

Soliman, Ahmed A.; Abdellah, Ahmed H.; Abou-Elheggag, N. A.; Abd-Elmougod, G. A.

doi:10.1016/j.csda.2012.01.025

Cited by 69 publications

(30 citation statements)

References 28 publications

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“…We would like to compute the MLE's of the unknown parameters. Before going to compute the MLE's, we plot the profile log-likelihood function (14) in Fig. 3.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, the MLE of α , say ˆ, α can be obtained by maximizing (14) with respect to α . The MLE α which maximizes (14) can be obtained from…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…For more applications about progressive-first-failure censoring data the readers may refer to Soliman et al [13] Soliman et al ( [14], [15] ), Soliman et al [16] and Ahmadi et al [17].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

Modhesh¹

2015

AJTAS

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Competing risks data usually arises in studies in which the death or failure of an individual or an item may be classified into one of T≥2 mutually exclusive causes. In this paper, we will study the competing risks model when the data is progressively first-failure-censored. Based on this type of censoring, we derive the maximum likelihood estimators (MLE's) for the unknown parameters. Approximate confidence intervals and two bootstrap confidence intervals are also proposed. The results in the cases of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are special cases. A real data set has been analyzed for illustrative purposes. Different methods have been compared using Monte Carlo simulations.

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“…We would like to compute the MLE's of the unknown parameters. Before going to compute the MLE's, we plot the profile log-likelihood function (14) in Fig. 3.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, the MLE of α , say ˆ, α can be obtained by maximizing (14) with respect to α . The MLE α which maximizes (14) can be obtained from…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

Modhesh¹

2015

AJTAS

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“…They obtained MLEs, interval estimation and expected time on test for the parameters of the Weibull distribution based on the progressive first-failure censored sample. Some recent studies on progressive firstfailure censoring scheme can be found in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Generalized inverted exponential distribution under progressive first-failure censoring

Dube

Krishna

Garg

2015

Journal of Statistical Computation and Simulation

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This article deals with progressive first-failure censoring, which is a generalization of progressive censoring. We derive maximum likelihood estimators of the unknown parameters and reliability characteristics of generalized inverted exponential distribution using progressive first-failure censored samples. The asymptotic confidence intervals and coverage probabilities for the parameters are obtained based on the observed Fisher's information matrix. Bayes estimators of the parameters and reliability characteristics under squared error loss function are obtained using the Lindley approximation and importance sampling methods. Also, highest posterior density credible intervals for the parameters are computed using importance sampling procedure. A Monte Carlo simulation study is conducted to analyse the performance of the estimators derived in the article. A real data set is discussed for illustration purposes. Finally, an optimal censoring scheme has been suggested using different optimality criteria.

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“…Figure 12 shows the OpenBUGS code for this "toy" example. Soliman et al (2012) show that the gamma distribution is an appropriate prior for the senescent component hazard in a Gompertz model, but they only do so after assuming a discrete prior for the baseline mortality. In their example they assume that values of from 0.05 up to 0.50 in steps of 0.05 are a priori equally likely.…”

Section: Model{mentioning

confidence: 99%

Bayes in biological anthropology

Konigsberg

Frankenberg

2013

American J Phys Anthropol

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In this article, we both contend and illustrate that biological anthropologists, particularly in the Americas, often think like Bayesians but act like frequentists when it comes to analyzing a wide variety of data. In other words, while our research goals and perspectives are rooted in probabilistic thinking and rest on prior knowledge, we often proceed to use statistical hypothesis tests and confidence interval methods unrelated (or tenuously related) to the research questions of interest. We advocate for applying Bayesian analyses to a number of different bioanthropological questions, especially since many of the programming and computational challenges to doing so have been overcome in the past two decades. To facilitate such applications, this article explains Bayesian principles and concepts, and provides concrete examples of Bayesian computer simulations and statistics that address questions relevant to biological anthropology, focusing particularly on bioarchaeology and forensic anthropology. It also simultaneously reviews the use of Bayesian methods and inference within the discipline to date. This article is intended to act as primer to Bayesian methods and inference in biological anthropology, explaining the relationships of various methods to likelihoods or probabilities and to classical statistical models. Our contention is not that traditional frequentist statistics should be rejected outright, but that there are many situations where biological anthropology is better served by taking a Bayesian approach. To this end it is hoped that the examples provided in this article will assist researchers in choosing from among the broad array of statistical methods currently available. Am J Phys Anthropol 57: 2013. V C 2013 Wiley Periodicals, Inc."The Bayesian approach can have a clarifying effect on one's thinking about evidence." (Koehler and Saks, 1991, p 364) Traditional training in statistical methods for those who go on to become practicing biological anthropologists has focused primarily on classical hypothesis testing. This is apparent in both textbooks geared toward anthropologists in general (Thomas, 1986;Madrigal, 1998;Bernard, 2011) and specialized texts for biological anthropologists (Slice, 2005;D'Aoãut and Vereecke, 2011). While Bayes' Theorem may be mentioned in passing in introductory statistics courses, this is typically restricted to examples of such limited interest that the student has little motivation to recall the theorem, and even less motivation to assume that there may be future value in having learned about Bayes' Theorem. In Bayesian terms, the prior probability that the student will retain Bayes' Theorem is quite low. In contrast, the student and eventual practitioner is likely to learn about confidence intervals, Type I and Type II errors in hypothesis testing, and P-values, and to blithely assume that what they have learned represents the near totality of what is available and useful within modern statistical practice. This represents an unfortunate omission of Ba...

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Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data

Cited by 69 publications

References 28 publications

Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

Generalized inverted exponential distribution under progressive first-failure censoring

Bayes in biological anthropology

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