Estimation and prediction of the Burr type XII distribution based on record values and inter-record times

Nadar, Mustafa; Kızılaslan, Fatih

doi:10.1080/00949655.2014.970554

Cited by 22 publications

(13 citation statements)

References 27 publications

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“…Bayesian prediction methods for future record values were first discussed by Dunsmore (1983) and have subsequently been applied to various distribution families [cf. Madi and Raqab (2004); Ahmadi and Doostparast (2006); Nadar and Kızılaslan (2015)]. It should be noted that, under exponential as well as under Pareto distributions, maximum likelihood prediction of the subsequent record value R r +1 becomes trivial, since the respective predictor is given by R r , i.e., the predictor coincides with the last observed record value in the model.…”

Section: Introductionmentioning

confidence: 99%

Maximum product of spacings prediction of future record values

Volovskiy

Kamps

2020

Metrika

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A spacings-based prediction method for future upper record values is proposed as an alternative to maximum likelihood prediction. For an underlying family of distributions with continuous cumulative distribution functions, the general form of the predictor as a function of the estimator of the distributional parameters is established. A connection between this method and the maximum observed likelihood prediction procedure is shown. The maximum product of spacings predictor turns out to be useful to predict the next record value in contrast to likelihood-based procedures, which provide trivial predictors in this particular case. Moreover, examples are given for the exponential and the Pareto distributions, and a real data set is analyzed.

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Section: Introductionmentioning

confidence: 99%

Maximum product of spacings prediction of future record values

Volovskiy

Kamps

2020

Metrika

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“…In the tables 3.11-3.14, we have discussed the limiting behavior of the variance covariance matrix obtained by inverting the fisher information matrix given in (11). As the analytical results of the Fisher information matrix for n cannot be obtained, we have calculated the entries of the Fisher information/variance covariance matrix by taking n = 5000 (extremely large).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This section discusses the asymptotic efficiencies and limiting information matrix when r n converges to, say, p which lies in (0,1) . According to Gupta et al (2004), for the left censored observations at the time point T , the limiting Fisher information matrix can be written as 11 Zheng and Gastwirth (2000) have shown that for location and scale family, the Fisher information matrix for Type-I and Type-II (both for left and right censored data) are asymptotically equivalent. They further described that for general case (not for location and scale family) the results for Type-II censored data (both for left and right) of the asymptotic Fisher information matrices are very difficult to obtain.…”

Section: Limiting Fisher Information Matrixmentioning

confidence: 99%

“…This property have motivated the authors to use this distribution for modeling extreme events such as flood frequencies, wind speeds, rainfalls and river discharge volumes. The details regarding these contributions can be seen from: Soliman (2002) Nadar and Alexandros (2011) and Feroze and Aslam (2012a). From other members of this family of distributions, the Bayesian analysis of Burr type VII and XI distributions have been discussed by Feroze and Aslam (2012b) and Feroze and Aslam (2012c) respectively.…”

Section: Introductionmentioning

confidence: 99%

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On Maximum Likelihood Estimation for Left Censored Burr Type III Distribution

Feroze

Aslam²,

Sindhu³

2015

Pak.j.stat.oper.res.

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Burr type III is an important distribution used to model the failure time data. The paper addresses the problem of estimation of parameters of the Burr type III distribution based on maximum likelihood estimation (MLE) when the samples are left censored. As the closed form expression for the MLEs of the parameters cannot be derived, the approximate solutions have been obtained through iterative procedures. An extensive simulation study has been carried out to investigate the performance of the estimators with respect to sample size, censoring rate and true parametric values. A real life example has also been presented. The study revealed that the proposed estimators are consistent and capable of providing efficient results under small to moderate samples. Pak.j.stat.oper.res. Vol.XI No.4 2015 pp497-512 498 Materials and MethodsThis section contains the derivation of maximum likelihood estimates, elements of Fisher information matrix, variance covariance matrix and confidence intervals for the parameters of the Burr type iii distribution under left censored samples. The limiting behavior of the Fisher information matrix has also been discussed. Maximum likelihood estimationBased on the left censored sample the likelihood function along with maximum likelihood estimators of the parameters of the Burr type iii distribution have been On Maximum Likelihood Estimation for Left Censored Burr Type III Distribution Pak.j.stat.oper.res. Vol.XI No.4 2015 pp497-512 499 discussed in the following. Let     1 ... rn XX  be the last nr  ordered statistics from the Burr type iii distribution. Then, the likelihood function for the sample of nr  left censored sample can be defined as:

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“…They present Bayesian inference under a squared error loss function by applying the Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples. [3] were discussed about the Bayes estimators for the parameters based on the upper records value.…”

Section: Introductionmentioning

confidence: 99%

Bound lengths for Burr-XII distribution under step-stress PALT

Prakash

2017

Int. J. Sci. World

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Some inferences based on Step-Stress Partially Accelerated Life Test (SS-PALT) are discussed in the present article. The Progressive Type-II censoring criterion with Random Removal scheme is used for determining the Approximate Confidence Lengths and One-Sample Bayes Prediction Bound Lengths for the unknown parameters of the Burr Type-XII distribution. Based on the simulated data, the analysis of the present discussion has been carried out.

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Estimation and prediction of the Burr type XII distribution based on record values and inter-record times

Cited by 22 publications

References 27 publications

Maximum product of spacings prediction of future record values

Maximum product of spacings prediction of future record values

On Maximum Likelihood Estimation for Left Censored Burr Type III Distribution

Bound lengths for Burr-XII distribution under step-stress PALT

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