The use of Burr type XII distribution on software reliability growth modelling

Abdel-Ghaly, Abdalla; AL-Dayian, G. R.; Al-Kashkari, F.H.

doi:10.1016/0026-2714(95)00124-7

Cited by 28 publications

(18 citation statements)

References 6 publications

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“…Zimav et al [4] showed that BXII distribution is a useful model for failure data in reliability studies. Some other usages of the BIII and BXII distributions can be found in [5][6][7][8][9][10]. However, BIII distribution is more ‡exible to …t data than BXII in the sense that it provides wider skewness and kurtosis region.…”

Section: Introductionmentioning

confidence: 99%

Statistical inference for the burr type III distribution under type II censored data

ÇANKAYA¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this study, estimation and prediction problems for the Burr type III distribution under type II censored data are considered. Maximum likelihood and maximum product spacing estimation methods are used to estimate model parameters. EM algorithm is employed to obtain maximum likelihood estimates. Unobserved future order statistics are predicted with best unbiased prediction method. A simulation study is carried out to exhibit performance of the estimation methods. Further, a numerical example is presented to illustrate the usefulness of the Burr III distribution.

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Section: Introductionmentioning

confidence: 99%

Statistical inference for the burr type III distribution under type II censored data

ÇANKAYA¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…These distributions have been used primarily for statistical modeling of events arising in a variety of applied mathematical contexts. Some examples of such applications include modeling events associated with forestry (Gove et al, 2008;Lindsay et al, 1996), fracture roughness (Nadarajah and Kotz, 2006Kotz, , 2007, life testing (Wingo, 1983(Wingo, , 1993, operational risk (Chernobai et al, 2007), option market price distributions (Sherrick et al, 1996), meteorology (Mielke, 1973), modeling crop prices (Tejeda and Goodwin, 2008), software reliability growth (Abdel-Ghaly et al, 1997), reliability analysis (Mokhlis, 2005), and in the context of Monte Carlo simulation studies Pant and Headrick, 2013).…”

Section: Introductionmentioning

confidence: 99%

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

Pant

Headrick

2016

Communications in Statistics - Simulation and Computation

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A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of (conventional) moments (MOM) in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating the Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios, tail-weight factors, and Spearman correlations. Simulation results demonstrate that the MOP-based Burr Type III and Type XII distributions are substantially superior to their (conventional) MOM-based counterparts in terms of relative bias and relative efficiency.

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“…Further, these distributions have been used in a variety of applied mathematics contexts. Some examples include modeling events associated with forestry [6,7], fracture roughness [8,9], life testing [10,11], operational risk [12], option market price distributions [13], meteorology [14], modeling crop prices [15], software reliability growth [16], reliability analysis [17], and in the context of Monte Carlo or simulation studies (e.g., [2]). …”

Section: Introductionmentioning

confidence: 99%

“…The shape of a Burr distribution associated with (2) or (3) is contingent on the values of the shape parameters ( and ), which can be determined by simultaneously solving equations (16) and (17) from [2, p. 2211] for given values of skew and kurtosis. In order for (2) or (3) to produce a valid Burr pdf, the quantile function ( ) is required to be a strictly increasing monotone function [2].…”

Section: Introductionmentioning

confidence: 99%

A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations

Pant

Headrick

2013

ISRN Applied Mathematics

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This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and thecorrelations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency-most notably when heavy-tailed distributions are of concern.

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The use of Burr type XII distribution on software reliability growth modelling

Cited by 28 publications

References 6 publications

Statistical inference for the burr type III distribution under type II censored data

Statistical inference for the burr type III distribution under type II censored data

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations

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