The Fisher information matrix for a three-parameter exponentiated Weibull distribution under type II censoring

Qian, Lianfen

doi:10.1016/j.stamet.2011.08.007

Cited by 21 publications

(20 citation statements)

References 12 publications

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“…Mudholkar and Srivasta [31] and Qian [35] show that this distribution allows both monotonic and bathtub shaped hazard rates. The latter shape is useful in reality.…”

Section: A Bi-ew Model and Its Aucmentioning

confidence: 98%

Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

Chang

Qian

2013

ISRN Probability and Statistics

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For a Bi-Exponentiated Weibull model, the authors obtain a general AUC formula and derive the maximum likelihood estimator of AUC and its asymptotic property. A simulation study is carried out to illustrate the finite sample size performance. ROC Curve and AUC for a Bi-Exponentiated Weibull ModelIn medical science, a diagnostic test result called a biomarker [1,2] is an indicator for disease status of patients. The accuracy of a medical diagnostic test is typically evaluated by sensitivity and specificity. Receiver Operating Characteristic (ROC) curve is a graphical representation of the relationship between sensitivity and specificity. The area under the ROC curve (AUC) is an overall performance measure for the biomarker. Hence the main issue in assessing the accuracy of a diagnostic test is to estimate the ROC curve and its AUC. Suppose that there are two groups of study subjects: diseased and nondiseased. Let be a continuous biomarker. Assume that the larger is, the more likely a subject is diseased. That is, a subject is classified as positive or diseased status if > and as negative or nondiseased status otherwise, where is a cutoff point. Let be the disease status:= 1 represents diseased population while = 0 represents nondiseased population. Sensitivity of is defined as the probability of being correctly classified as disease status and specificity as the probability of being correctly classified as nondisease status. That is, sensitivity ( ) = ( > | = 1) , specificity ( ) = ( < | = 0) .(1) Let = { | = 1} and = { | = 0} be the biomarkers for diseased and nondiseased subjects with survival functions 1 and 0 , respectively. Then sensitivity ( ) = 1 ( ) ,The ROC function (curve) is defined asNotice that ROC curve is a monotonic increasing curve in a unit square starting at (0, 0) and ending at (1, 1). A good biomarker has a very concave down ROC curve. We say a bivariate random vector ( , ) is a Bi-model if and are independent and are from the same distribution family but with different parameters. Pepe [3] summarizes ROC analysis and notices that among Bi-model, Bi-normal model has been the most popular one. The ROC curve method traces back to Green and Swets [4] in the signal detection theory. Bi-normal model assumes the existence of a monotonic increasing transformation such that the biomarker can be transformed into normally distributed for both diseased and nondiseased patients. Pepe [3, Results 4.1 and 4.4] shows that the ROC curve of a biomarker is invariant under a monotone increasing transformation. Hence, a good estimator of ROC curve should satisfy this invariance property.

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“…Mudholkar and Srivasta [31] and Qian [35] show that this distribution allows both monotonic and bathtub shaped hazard rates. The latter shape is useful in reality.…”

Section: A Bi-ew Model and Its Aucmentioning

confidence: 98%

Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

Chang

Qian

2013

ISRN Probability and Statistics

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“…The fiber data has been analyzed by several other authors too, including Lemonte and Cordeiro [14], Qian [24] and Shams [28].…”

Section: Real Data Applicationmentioning

confidence: 99%

“…Qian [24] fitted the exponentiated exponential distribution (equivalent to the parallelparallel-f 0 -exponential distribution with N ≡ 1) and obtained the estimates α = 7.788, β = 1.013. These estimates have the interpretation that breaking stress of a fiber is that of a system having 7.8 number of components working in parallel, where the failure time of each component has an exponential distribution with mean equal to 0.987.…”

Section: Real Data Applicationmentioning

confidence: 99%

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Compound geometric and Poisson models

Hakamipour¹,

Rezaei²,

Nadarajah³

2015

Kybernetika

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“…This scheme is often adopted for toxicology experiments and life testing applications by engineers as it has been proven to save time and money. Several authors have addressed inferential issues based on Type-II censored samples; see for example, [13], [2], [19], [3], [9], [16], [11], [17], and [10]. Their research results for estimating parameters of different lifetime distributions under Type-II censoring are limited to precise data.…”

Section: Introductionmentioning

confidence: 99%

Estimating the parameter of Exponential distribution under Type-II censoring from fuzzy data

Khoolenjani¹,

Shahsanaie²

2016

JSTA

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Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. This paper deals with the estimation of exponential mean parameter under Type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. We use Newton-Raphson algorithm as well as EM algorithm to determine the maximum likelihood estimate (MLE) of parameter. We also obtain the estimate, via moment method and Bayesian procedure, of the unknown parameter. In addition, a new numerical method for parameter estimation is provided. Monte Carlo simulations are performed to investigate performance of the different methods. Finally, an example is presented in order to illustrate the methods of inference discussed here.

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The Fisher information matrix for a three-parameter exponentiated Weibull distribution under type II censoring

Cited by 21 publications

References 12 publications

Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

Compound geometric and Poisson models

Estimating the parameter of Exponential distribution under Type-II censoring from fuzzy data

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