The burr distribution and quantal responses

Drane, J. Wanzer; Owen, D. B.; Seibert, Guy Burton

doi:10.1007/bf02932803

Cited by 9 publications

(2 citation statements)

References 11 publications

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“…). Further details on the Burr XII distribution can be found in [7], [22], [25], [10], [19], [5], [15] and [1]. Consequently, numerous modification or generalizations of the BXII distribution, using different compounding and weighting techniques, have been suggested.…”

Section: Introductionmentioning

confidence: 99%

On a modified Burr XII distribution having flexible hazard rate shapes

Jamal

Chesneau

Nasir³

et al. 2020

Mathematica Slovaca

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In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.

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Section: Introductionmentioning

confidence: 99%

On a modified Burr XII distribution having flexible hazard rate shapes

Jamal

Chesneau

Nasir³

et al. 2020

Mathematica Slovaca

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“…That is, if X|θ~ Weibull (θ, β) and θ~ gamma (γ, δ) then the compound PDF, say g(x|β, γ, δ), is given by The Burr XII and its reciprocal Burr III distributions have been used in many applications such as actuarial science, as in Embrechts et al [7] and Klugman [8], quantal bioassay as in Drane et al [9], economics, as in McDonald and Richards [10], Morrison and Schmittlein ,  [11], Schmittlein [12], McDonald [13], forestry,as in Lindsay et al [14], exotoxicology, as in Shao [15], life testing and reliability, as in Dubey [16,17], Papadopoulos [18], Lewis [19], Evans and Ragab [20], Lingappaiah [21], Jaheen [22], AL-Hussaini et al [23], Shah and Gokhale [24], AL-Hussaini and Jaheen, [25,26] and Moore and Papadopoulos [27], among others. Khan and Khan [28] and AL-Hussaini [29] characterized the Burr XII distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation Using Censored Data from Exponentiated Burr Type XII Population

AL-Hussaini¹,

Hussein²

2011

OJS

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Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme. Bayes estimators have been developed using the standard Bayes and MCMC methods under square error and LINEX loss functions, using informative type of priors for the parameters. Simulation comparison of various estimation methods is made when n = 20, 40, 60 and censored data. The Bayes estimates are found to be, generally, better than the maximum likelihood estimates against the proposed prior, in the sense of having smaller mean square errors. This is found to be true whether the data are complete or censored. Estimates improve by increasing sample size. Analysis is also carried out for real life data.

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Burr Distributions

Rodriguez

2004

Encyclopedia of Statistical Sciences

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The burr distribution and quantal responses

Cited by 9 publications

References 11 publications

On a modified Burr XII distribution having flexible hazard rate shapes

On a modified Burr XII distribution having flexible hazard rate shapes

Estimation Using Censored Data from Exponentiated Burr Type XII Population

Burr Distributions

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